30 years of collaboration View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2016-10-15

AUTHORS

Clemens Fuchs, Lajos Hajdu

ABSTRACT

We highlight some of the most important cornerstones of the long standing and very fruitful collaboration of the Austrian Diophantine Number Theory research group and the Number Theory and Cryptography School of Debrecen. However, we do not plan to be complete in any sense but give some interesting data and selected results that we find particularly nice. At the end we focus on two topics in more detail, namely a problem that origins from a conjecture of Rényi and Erdős (on the number of terms of the square of a polynomial) and another one that origins from a question of Zelinsky (on the unit sum number problem). This paper evolved from a plenary invited talk that the authors gave at the Joint Austrian-Hungarian Mathematical Conference 2015, August 25–27, 2015 in Győr (Hungary). More... »

PAGES

255-274

References to SciGraph publications

  • <error retrieving object. in <ERROR RETRIEVING OBJECT
  • 1965-02. Wie der Beweis der Vermutung von Baudet gefunden wurde in ABHANDLUNGEN AUS DEM MATHEMATISCHEN SEMINAR DER UNIVERSITÄT HAMBURG
  • 1995-12. Complete solution of a family of quartic Thue equations in ABHANDLUNGEN AUS DEM MATHEMATISCHEN SEMINAR DER UNIVERSITÄT HAMBURG
  • 2008-01-01. On the Diophantine Equation Gn(x) = Gm(y) with Q (x, y)=0 in DIOPHANTINE APPROXIMATION
  • 2015-06-20. On conjectures and problems of Ruzsa concerning difference graphs of S-units in ACTA MATHEMATICA HUNGARICA
  • 2002-11. On the Diophantine Equation Gn(x) = Gm(P(x)) in MONATSHEFTE FÜR MATHEMATIK
  • 2001-04. On Explicit Bounds for the Solutions of a Class of Parametrized Thue Equations of Arbitrary Degree in MONATSHEFTE FÜR MATHEMATIK
  • 2005-12. On a family of cubics over imaginary quadratic fields</o:p> in PERIODICA MATHEMATICA HUNGARICA
  • 2008-04-24. On composite lacunary polynomials and the proof of a conjecture of Schinzel in INVENTIONES MATHEMATICAE
  • 2000-11. A Parametric Family of Quintic Thue Equations II in MONATSHEFTE FÜR MATHEMATIK
  • 1972-06. Almost diagonal matrices over Dedekind domains in MATHEMATISCHE ZEITSCHRIFT
  • 2000-06. Octahedrons with Equally Many Lattice Points in PERIODICA MATHEMATICA HUNGARICA
  • 2002-04. Diophantine Equations and Bernoulli Polynomials in COMPOSITIO MATHEMATICA
  • 2012-01-08. Variables separated equations: Strikingly different roles for the Branch Cycle Lemma and the finite simple group classification in SCIENCE CHINA MATHEMATICS
  • 1981-12. Canonical number systems in algebraic number fields in ACTA MATHEMATICA HUNGARICA
  • 2005-08. Generalized radix representations and dynamical systems. I in ACTA MATHEMATICA HUNGARICA
  • 1997-01. Fractal digital sums and codes in APPLICABLE ALGEBRA IN ENGINEERING, COMMUNICATION AND COMPUTING
  • 2009. Combinatorial Number Theory and Additive Group Theory in NONE
  • 1997-06. Fast gaussian random number generation using linear transformations in COMPUTING
  • 2009-09-02. On quantitative aspects of the unit sum number problem in ARCHIV DER MATHEMATIK
  • 2016-01-09. Elementary resolution of a family of quartic Thue equations over function fields in MONATSHEFTE FÜR MATHEMATIK
  • 2010-04-13. Sums of units in function fields in MONATSHEFTE FÜR MATHEMATIK
  • 1991. Diophantine Approximations and Diophantine Equations in NONE
  • 2006-03. Remarks on a conjecture on certain integer sequences in PERIODICA MATHEMATICA HUNGARICA
  • 1994-09. A note on Thue's equation over function fields in MONATSHEFTE FÜR MATHEMATIK
  • 2007-01-31. On Sums of Units in MONATSHEFTE FÜR MATHEMATIK
  • 1981-03. Canonical number systems in imaginary quadratic fields in ACTA MATHEMATICA HUNGARICA
  • 1998-01. On a Diophantine Equation Concerning the Number of Integer Points in Special Domains in ACTA MATHEMATICA HUNGARICA
  • 2011-04-07. On biquadratic fields that admit unit power integral basis in ACTA MATHEMATICA HUNGARICA
  • 2013-10-01. On sums of S-integers of bounded norm in MONATSHEFTE FÜR MATHEMATIK
  • 2014-01-24. Representing algebraic integers as linear combinations of units in PERIODICA MATHEMATICA HUNGARICA
  • 2007-06. Arithmetic Progressions in Linear Combinations of S-Units in PERIODICA MATHEMATICA HUNGARICA
  • 2005-11-16. On a Family of Thue Equations Over Function Fields in MONATSHEFTE FÜR MATHEMATIK
  • 1983-03. Bounds for the solutions of norm form, discriminant form and index form equations in finitely generated integral domains in ACTA MATHEMATICA HUNGARICA
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s10998-016-0158-8

    DOI

    http://dx.doi.org/10.1007/s10998-016-0158-8

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1041250860


    Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
    Incoming Citations Browse incoming citations for this publication using opencitations.net

    JSON-LD is the canonical representation for SciGraph data.

    TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

    [
      {
        "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
        "about": [
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Mathematical Sciences", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Pure Mathematics", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "Department of Mathematics, University of Salzburg, Hellbrunner Str. 34/I, 5020, Salzburg, Austria", 
              "id": "http://www.grid.ac/institutes/grid.7039.d", 
              "name": [
                "Department of Mathematics, University of Salzburg, Hellbrunner Str. 34/I, 5020, Salzburg, Austria"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Fuchs", 
            "givenName": "Clemens", 
            "id": "sg:person.011534256073.49", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011534256073.49"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Institute of Mathematics, University of Debrecen, P.O. Box 12, 4010, Debrecen, Hungary", 
              "id": "http://www.grid.ac/institutes/grid.7122.6", 
              "name": [
                "Institute of Mathematics, University of Debrecen, P.O. Box 12, 4010, Debrecen, Hungary"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Hajdu", 
            "givenName": "Lajos", 
            "id": "sg:person.011313751427.99", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011313751427.99"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1023/a:1010399929053", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1004466615", 
              "https://doi.org/10.1023/a:1010399929053"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bfb0098246", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1049870206", 
              "https://doi.org/10.1007/bfb0098246"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01279308", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1046846312", 
              "https://doi.org/10.1007/bf01279308"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s-10998-007-2175-8", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1084017856", 
              "https://doi.org/10.1007/s-10998-007-2175-8"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02684478", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1023101854", 
              "https://doi.org/10.1007/bf02684478"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s11425-011-4324-4", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1026440177", 
              "https://doi.org/10.1007/s11425-011-4324-4"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-7643-8962-8", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1016796537", 
              "https://doi.org/10.1007/978-3-7643-8962-8"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00605-006-0402-z", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1015657696", 
              "https://doi.org/10.1007/s00605-006-0402-z"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s006050170037", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1033630814", 
              "https://doi.org/10.1007/s006050170037"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s006050070022", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1000521608", 
              "https://doi.org/10.1007/s006050070022"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02953340", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1004982842", 
              "https://doi.org/10.1007/bf02953340"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00605-013-0574-2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1051027756", 
              "https://doi.org/10.1007/s00605-013-0574-2"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10474-015-0513-x", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1049246026", 
              "https://doi.org/10.1007/s10474-015-0513-x"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01895142", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1050389700", 
              "https://doi.org/10.1007/bf01895142"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00605-002-0497-9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1019283551", 
              "https://doi.org/10.1007/s00605-002-0497-9"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10998-005-0032-6", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1009409967", 
              "https://doi.org/10.1007/s10998-005-0032-6"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1023/a:1006518403429", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1027732299", 
              "https://doi.org/10.1023/a:1006518403429"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00605-005-0330-3", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1032124782", 
              "https://doi.org/10.1007/s00605-005-0330-3"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1023/a:1014972217217", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1006077877", 
              "https://doi.org/10.1023/a:1014972217217"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02993133", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1004844479", 
              "https://doi.org/10.1007/bf02993133"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01301690", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1001108361", 
              "https://doi.org/10.1007/bf01301690"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00605-010-0219-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1027975443", 
              "https://doi.org/10.1007/s00605-010-0219-7"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10998-014-0020-9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1000821575", 
              "https://doi.org/10.1007/s10998-014-0020-9"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/978-3-211-74280-8_10", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1022121577", 
              "https://doi.org/10.1007/978-3-211-74280-8_10"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10998-006-0002-7", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1046571840", 
              "https://doi.org/10.1007/s10998-006-0002-7"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00013-009-0037-0", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1016513051", 
              "https://doi.org/10.1007/s00013-009-0037-0"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00605-012-0391-z", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1026499799", 
              "https://doi.org/10.1007/s00605-012-0391-z"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10474-011-0103-5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1049769546", 
              "https://doi.org/10.1007/s10474-011-0103-5"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01904880", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1050650815", 
              "https://doi.org/10.1007/bf01904880"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00605-015-0864-y", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1033783608", 
              "https://doi.org/10.1007/s00605-015-0864-y"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00222-008-0136-8", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1006053189", 
              "https://doi.org/10.1007/s00222-008-0136-8"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10474-005-0221-z", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1047907570", 
              "https://doi.org/10.1007/s10474-005-0221-z"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s002000050050", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1036076666", 
              "https://doi.org/10.1007/s002000050050"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01960551", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1048769637", 
              "https://doi.org/10.1007/bf01960551"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2016-10-15", 
        "datePublishedReg": "2016-10-15", 
        "description": "We highlight some of the most important cornerstones of the long standing and very fruitful collaboration of the Austrian Diophantine Number Theory research group and the Number Theory and Cryptography School of Debrecen. However, we do not plan to be complete in any sense but give some interesting data and selected results that we find particularly nice. At the end we focus on two topics in more detail, namely a problem that origins from a conjecture of R\u00e9nyi and Erd\u0151s (on the number of terms of the square of a polynomial) and another one that origins from a question of Zelinsky (on the unit sum number problem). This paper evolved from a plenary invited talk that the authors gave at the Joint Austrian-Hungarian Mathematical Conference 2015, August 25\u201327, 2015 in Gy\u0151r (Hungary).", 
        "genre": "article", 
        "id": "sg:pub.10.1007/s10998-016-0158-8", 
        "inLanguage": "en", 
        "isAccessibleForFree": false, 
        "isFundedItemOf": [
          {
            "id": "sg:grant.6206592", 
            "type": "MonetaryGrant"
          }, 
          {
            "id": "sg:grant.4193658", 
            "type": "MonetaryGrant"
          }, 
          {
            "id": "sg:grant.4323047", 
            "type": "MonetaryGrant"
          }, 
          {
            "id": "sg:grant.6208024", 
            "type": "MonetaryGrant"
          }
        ], 
        "isPartOf": [
          {
            "id": "sg:journal.1136293", 
            "issn": [
              "0031-5303", 
              "1588-2829"
            ], 
            "name": "Periodica Mathematica Hungarica", 
            "publisher": "Springer Nature", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "2", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "74"
          }
        ], 
        "keywords": [
          "number theory", 
          "R\u00e9nyi", 
          "conjecture", 
          "Erd\u0151s", 
          "problem", 
          "theory", 
          "fruitful collaboration", 
          "more detail", 
          "sense", 
          "years of collaboration", 
          "Gy\u0151r", 
          "one", 
          "Zelinsky", 
          "long standing", 
          "detail", 
          "results", 
          "topic", 
          "data", 
          "questions", 
          "research groups", 
          "authors", 
          "end", 
          "talk", 
          "cornerstone", 
          "interesting data", 
          "plenary", 
          "collaboration", 
          "group", 
          "standing", 
          "years", 
          "schools", 
          "important cornerstone", 
          "Debrecen", 
          "paper", 
          "Austrian Diophantine Number Theory research group", 
          "Diophantine Number Theory research group", 
          "Number Theory research group", 
          "Theory research group", 
          "Cryptography School", 
          "conjecture of R\u00e9nyi", 
          "question of Zelinsky", 
          "Hungarian Mathematical Conference 2015", 
          "Mathematical Conference 2015", 
          "Conference 2015"
        ], 
        "name": "30 years of collaboration", 
        "pagination": "255-274", 
        "productId": [
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1041250860"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/s10998-016-0158-8"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/s10998-016-0158-8", 
          "https://app.dimensions.ai/details/publication/pub.1041250860"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2022-01-01T18:39", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-springernature-scigraph/baseset/20220101/entities/gbq_results/article/article_706.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "https://doi.org/10.1007/s10998-016-0158-8"
      }
    ]
     

    Download the RDF metadata as:  json-ld nt turtle xml License info

    HOW TO GET THIS DATA PROGRAMMATICALLY:

    JSON-LD is a popular format for linked data which is fully compatible with JSON.

    curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s10998-016-0158-8'

    N-Triples is a line-based linked data format ideal for batch operations.

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s10998-016-0158-8'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s10998-016-0158-8'

    RDF/XML is a standard XML format for linked data.

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s10998-016-0158-8'


     

    This table displays all metadata directly associated to this object as RDF triples.

    256 TRIPLES      22 PREDICATES      103 URIs      61 LITERALS      6 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/s10998-016-0158-8 schema:about anzsrc-for:01
    2 anzsrc-for:0101
    3 schema:author N1951d34fba6e4fc0b9e3f446b07773df
    4 schema:citation sg:pub.10.1007/978-3-211-74280-8_10
    5 sg:pub.10.1007/978-3-7643-8962-8
    6 sg:pub.10.1007/bf01279308
    7 sg:pub.10.1007/bf01301690
    8 sg:pub.10.1007/bf01895142
    9 sg:pub.10.1007/bf01904880
    10 sg:pub.10.1007/bf01960551
    11 sg:pub.10.1007/bf02684478
    12 sg:pub.10.1007/bf02953340
    13 sg:pub.10.1007/bf02993133
    14 sg:pub.10.1007/bfb0098246
    15 sg:pub.10.1007/s-10998-007-2175-8
    16 sg:pub.10.1007/s00013-009-0037-0
    17 sg:pub.10.1007/s002000050050
    18 sg:pub.10.1007/s00222-008-0136-8
    19 sg:pub.10.1007/s00605-002-0497-9
    20 sg:pub.10.1007/s00605-005-0330-3
    21 sg:pub.10.1007/s00605-006-0402-z
    22 sg:pub.10.1007/s00605-010-0219-7
    23 sg:pub.10.1007/s00605-012-0391-z
    24 sg:pub.10.1007/s00605-013-0574-2
    25 sg:pub.10.1007/s00605-015-0864-y
    26 sg:pub.10.1007/s006050070022
    27 sg:pub.10.1007/s006050170037
    28 sg:pub.10.1007/s10474-005-0221-z
    29 sg:pub.10.1007/s10474-011-0103-5
    30 sg:pub.10.1007/s10474-015-0513-x
    31 sg:pub.10.1007/s10998-005-0032-6
    32 sg:pub.10.1007/s10998-006-0002-7
    33 sg:pub.10.1007/s10998-014-0020-9
    34 sg:pub.10.1007/s11425-011-4324-4
    35 sg:pub.10.1023/a:1006518403429
    36 sg:pub.10.1023/a:1010399929053
    37 sg:pub.10.1023/a:1014972217217
    38 schema:datePublished 2016-10-15
    39 schema:datePublishedReg 2016-10-15
    40 schema:description We highlight some of the most important cornerstones of the long standing and very fruitful collaboration of the Austrian Diophantine Number Theory research group and the Number Theory and Cryptography School of Debrecen. However, we do not plan to be complete in any sense but give some interesting data and selected results that we find particularly nice. At the end we focus on two topics in more detail, namely a problem that origins from a conjecture of Rényi and Erdős (on the number of terms of the square of a polynomial) and another one that origins from a question of Zelinsky (on the unit sum number problem). This paper evolved from a plenary invited talk that the authors gave at the Joint Austrian-Hungarian Mathematical Conference 2015, August 25–27, 2015 in Győr (Hungary).
    41 schema:genre article
    42 schema:inLanguage en
    43 schema:isAccessibleForFree false
    44 schema:isPartOf N902def1121e840fb888beabdc99409fc
    45 Ne24d58babab04cceb2ccf9b6d517b192
    46 sg:journal.1136293
    47 schema:keywords Austrian Diophantine Number Theory research group
    48 Conference 2015
    49 Cryptography School
    50 Debrecen
    51 Diophantine Number Theory research group
    52 Erdős
    53 Győr
    54 Hungarian Mathematical Conference 2015
    55 Mathematical Conference 2015
    56 Number Theory research group
    57 Rényi
    58 Theory research group
    59 Zelinsky
    60 authors
    61 collaboration
    62 conjecture
    63 conjecture of Rényi
    64 cornerstone
    65 data
    66 detail
    67 end
    68 fruitful collaboration
    69 group
    70 important cornerstone
    71 interesting data
    72 long standing
    73 more detail
    74 number theory
    75 one
    76 paper
    77 plenary
    78 problem
    79 question of Zelinsky
    80 questions
    81 research groups
    82 results
    83 schools
    84 sense
    85 standing
    86 talk
    87 theory
    88 topic
    89 years
    90 years of collaboration
    91 schema:name 30 years of collaboration
    92 schema:pagination 255-274
    93 schema:productId N689f3ccd35354cb49a55ce88f5dc978a
    94 Neecc6ee83cfc4588929fcf6f1e2f54b1
    95 schema:sameAs https://app.dimensions.ai/details/publication/pub.1041250860
    96 https://doi.org/10.1007/s10998-016-0158-8
    97 schema:sdDatePublished 2022-01-01T18:39
    98 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    99 schema:sdPublisher N141e5412561d4b58b662427b4bd0106b
    100 schema:url https://doi.org/10.1007/s10998-016-0158-8
    101 sgo:license sg:explorer/license/
    102 sgo:sdDataset articles
    103 rdf:type schema:ScholarlyArticle
    104 N141e5412561d4b58b662427b4bd0106b schema:name Springer Nature - SN SciGraph project
    105 rdf:type schema:Organization
    106 N1951d34fba6e4fc0b9e3f446b07773df rdf:first sg:person.011534256073.49
    107 rdf:rest N4a59f5dda59149fabbf0072a2b0a6433
    108 N4a59f5dda59149fabbf0072a2b0a6433 rdf:first sg:person.011313751427.99
    109 rdf:rest rdf:nil
    110 N689f3ccd35354cb49a55ce88f5dc978a schema:name dimensions_id
    111 schema:value pub.1041250860
    112 rdf:type schema:PropertyValue
    113 N902def1121e840fb888beabdc99409fc schema:issueNumber 2
    114 rdf:type schema:PublicationIssue
    115 Ne24d58babab04cceb2ccf9b6d517b192 schema:volumeNumber 74
    116 rdf:type schema:PublicationVolume
    117 Neecc6ee83cfc4588929fcf6f1e2f54b1 schema:name doi
    118 schema:value 10.1007/s10998-016-0158-8
    119 rdf:type schema:PropertyValue
    120 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    121 schema:name Mathematical Sciences
    122 rdf:type schema:DefinedTerm
    123 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
    124 schema:name Pure Mathematics
    125 rdf:type schema:DefinedTerm
    126 sg:grant.4193658 http://pending.schema.org/fundedItem sg:pub.10.1007/s10998-016-0158-8
    127 rdf:type schema:MonetaryGrant
    128 sg:grant.4323047 http://pending.schema.org/fundedItem sg:pub.10.1007/s10998-016-0158-8
    129 rdf:type schema:MonetaryGrant
    130 sg:grant.6206592 http://pending.schema.org/fundedItem sg:pub.10.1007/s10998-016-0158-8
    131 rdf:type schema:MonetaryGrant
    132 sg:grant.6208024 http://pending.schema.org/fundedItem sg:pub.10.1007/s10998-016-0158-8
    133 rdf:type schema:MonetaryGrant
    134 sg:journal.1136293 schema:issn 0031-5303
    135 1588-2829
    136 schema:name Periodica Mathematica Hungarica
    137 schema:publisher Springer Nature
    138 rdf:type schema:Periodical
    139 sg:person.011313751427.99 schema:affiliation grid-institutes:grid.7122.6
    140 schema:familyName Hajdu
    141 schema:givenName Lajos
    142 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011313751427.99
    143 rdf:type schema:Person
    144 sg:person.011534256073.49 schema:affiliation grid-institutes:grid.7039.d
    145 schema:familyName Fuchs
    146 schema:givenName Clemens
    147 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011534256073.49
    148 rdf:type schema:Person
    149 sg:pub.10.1007/978-3-211-74280-8_10 schema:sameAs https://app.dimensions.ai/details/publication/pub.1022121577
    150 https://doi.org/10.1007/978-3-211-74280-8_10
    151 rdf:type schema:CreativeWork
    152 sg:pub.10.1007/978-3-7643-8962-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1016796537
    153 https://doi.org/10.1007/978-3-7643-8962-8
    154 rdf:type schema:CreativeWork
    155 sg:pub.10.1007/bf01279308 schema:sameAs https://app.dimensions.ai/details/publication/pub.1046846312
    156 https://doi.org/10.1007/bf01279308
    157 rdf:type schema:CreativeWork
    158 sg:pub.10.1007/bf01301690 schema:sameAs https://app.dimensions.ai/details/publication/pub.1001108361
    159 https://doi.org/10.1007/bf01301690
    160 rdf:type schema:CreativeWork
    161 sg:pub.10.1007/bf01895142 schema:sameAs https://app.dimensions.ai/details/publication/pub.1050389700
    162 https://doi.org/10.1007/bf01895142
    163 rdf:type schema:CreativeWork
    164 sg:pub.10.1007/bf01904880 schema:sameAs https://app.dimensions.ai/details/publication/pub.1050650815
    165 https://doi.org/10.1007/bf01904880
    166 rdf:type schema:CreativeWork
    167 sg:pub.10.1007/bf01960551 schema:sameAs https://app.dimensions.ai/details/publication/pub.1048769637
    168 https://doi.org/10.1007/bf01960551
    169 rdf:type schema:CreativeWork
    170 sg:pub.10.1007/bf02684478 schema:sameAs https://app.dimensions.ai/details/publication/pub.1023101854
    171 https://doi.org/10.1007/bf02684478
    172 rdf:type schema:CreativeWork
    173 sg:pub.10.1007/bf02953340 schema:sameAs https://app.dimensions.ai/details/publication/pub.1004982842
    174 https://doi.org/10.1007/bf02953340
    175 rdf:type schema:CreativeWork
    176 sg:pub.10.1007/bf02993133 schema:sameAs https://app.dimensions.ai/details/publication/pub.1004844479
    177 https://doi.org/10.1007/bf02993133
    178 rdf:type schema:CreativeWork
    179 sg:pub.10.1007/bfb0098246 schema:sameAs https://app.dimensions.ai/details/publication/pub.1049870206
    180 https://doi.org/10.1007/bfb0098246
    181 rdf:type schema:CreativeWork
    182 sg:pub.10.1007/s-10998-007-2175-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1084017856
    183 https://doi.org/10.1007/s-10998-007-2175-8
    184 rdf:type schema:CreativeWork
    185 sg:pub.10.1007/s00013-009-0037-0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1016513051
    186 https://doi.org/10.1007/s00013-009-0037-0
    187 rdf:type schema:CreativeWork
    188 sg:pub.10.1007/s002000050050 schema:sameAs https://app.dimensions.ai/details/publication/pub.1036076666
    189 https://doi.org/10.1007/s002000050050
    190 rdf:type schema:CreativeWork
    191 sg:pub.10.1007/s00222-008-0136-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006053189
    192 https://doi.org/10.1007/s00222-008-0136-8
    193 rdf:type schema:CreativeWork
    194 sg:pub.10.1007/s00605-002-0497-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1019283551
    195 https://doi.org/10.1007/s00605-002-0497-9
    196 rdf:type schema:CreativeWork
    197 sg:pub.10.1007/s00605-005-0330-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1032124782
    198 https://doi.org/10.1007/s00605-005-0330-3
    199 rdf:type schema:CreativeWork
    200 sg:pub.10.1007/s00605-006-0402-z schema:sameAs https://app.dimensions.ai/details/publication/pub.1015657696
    201 https://doi.org/10.1007/s00605-006-0402-z
    202 rdf:type schema:CreativeWork
    203 sg:pub.10.1007/s00605-010-0219-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1027975443
    204 https://doi.org/10.1007/s00605-010-0219-7
    205 rdf:type schema:CreativeWork
    206 sg:pub.10.1007/s00605-012-0391-z schema:sameAs https://app.dimensions.ai/details/publication/pub.1026499799
    207 https://doi.org/10.1007/s00605-012-0391-z
    208 rdf:type schema:CreativeWork
    209 sg:pub.10.1007/s00605-013-0574-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1051027756
    210 https://doi.org/10.1007/s00605-013-0574-2
    211 rdf:type schema:CreativeWork
    212 sg:pub.10.1007/s00605-015-0864-y schema:sameAs https://app.dimensions.ai/details/publication/pub.1033783608
    213 https://doi.org/10.1007/s00605-015-0864-y
    214 rdf:type schema:CreativeWork
    215 sg:pub.10.1007/s006050070022 schema:sameAs https://app.dimensions.ai/details/publication/pub.1000521608
    216 https://doi.org/10.1007/s006050070022
    217 rdf:type schema:CreativeWork
    218 sg:pub.10.1007/s006050170037 schema:sameAs https://app.dimensions.ai/details/publication/pub.1033630814
    219 https://doi.org/10.1007/s006050170037
    220 rdf:type schema:CreativeWork
    221 sg:pub.10.1007/s10474-005-0221-z schema:sameAs https://app.dimensions.ai/details/publication/pub.1047907570
    222 https://doi.org/10.1007/s10474-005-0221-z
    223 rdf:type schema:CreativeWork
    224 sg:pub.10.1007/s10474-011-0103-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1049769546
    225 https://doi.org/10.1007/s10474-011-0103-5
    226 rdf:type schema:CreativeWork
    227 sg:pub.10.1007/s10474-015-0513-x schema:sameAs https://app.dimensions.ai/details/publication/pub.1049246026
    228 https://doi.org/10.1007/s10474-015-0513-x
    229 rdf:type schema:CreativeWork
    230 sg:pub.10.1007/s10998-005-0032-6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1009409967
    231 https://doi.org/10.1007/s10998-005-0032-6
    232 rdf:type schema:CreativeWork
    233 sg:pub.10.1007/s10998-006-0002-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1046571840
    234 https://doi.org/10.1007/s10998-006-0002-7
    235 rdf:type schema:CreativeWork
    236 sg:pub.10.1007/s10998-014-0020-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1000821575
    237 https://doi.org/10.1007/s10998-014-0020-9
    238 rdf:type schema:CreativeWork
    239 sg:pub.10.1007/s11425-011-4324-4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1026440177
    240 https://doi.org/10.1007/s11425-011-4324-4
    241 rdf:type schema:CreativeWork
    242 sg:pub.10.1023/a:1006518403429 schema:sameAs https://app.dimensions.ai/details/publication/pub.1027732299
    243 https://doi.org/10.1023/a:1006518403429
    244 rdf:type schema:CreativeWork
    245 sg:pub.10.1023/a:1010399929053 schema:sameAs https://app.dimensions.ai/details/publication/pub.1004466615
    246 https://doi.org/10.1023/a:1010399929053
    247 rdf:type schema:CreativeWork
    248 sg:pub.10.1023/a:1014972217217 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006077877
    249 https://doi.org/10.1023/a:1014972217217
    250 rdf:type schema:CreativeWork
    251 grid-institutes:grid.7039.d schema:alternateName Department of Mathematics, University of Salzburg, Hellbrunner Str. 34/I, 5020, Salzburg, Austria
    252 schema:name Department of Mathematics, University of Salzburg, Hellbrunner Str. 34/I, 5020, Salzburg, Austria
    253 rdf:type schema:Organization
    254 grid-institutes:grid.7122.6 schema:alternateName Institute of Mathematics, University of Debrecen, P.O. Box 12, 4010, Debrecen, Hungary
    255 schema:name Institute of Mathematics, University of Debrecen, P.O. Box 12, 4010, Debrecen, Hungary
    256 rdf:type schema:Organization
     




    Preview window. Press ESC to close (or click here)


    ...