On the Finiteness of Hyperelliptic Fields with Special Properties and Periodic Expansion of √f View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2018-11

AUTHORS

V. P. Platonov, V. S. Zhgoon, M. M. Petrunin, Yu. N. Shteinikov

ABSTRACT

We prove the finiteness of the set of square-free polynomials f ∈ k[x] of odd degree distinct from 11 considered up to a natural equivalence relation for which the continued fraction expansion of the irrationality f(x) in k((x)) is periodic and the corresponding hyperelliptic field k(x)(√f) contains an S-unit of degree 11. Moreover, it was proved for k = ℚ that there are no polynomials of odd degree distinct from 9 and 11 satisfying the conditions mentioned above. More... »

PAGES

641-645

Journal

TITLE

Doklady Mathematics

ISSUE

3

VOLUME

98

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1134/s1064562418070281

DOI

http://dx.doi.org/10.1134/s1064562418070281

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1111224425


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/2008/0101", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Pure Mathematics", 
        "type": "DefinedTerm"
      }, 
      {
        "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"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Russian Academy of Sciences", 
          "id": "https://www.grid.ac/institutes/grid.4886.2", 
          "name": [
            "Scientific Research Institute for System Analysis, Russian Academy of Sciences, 117218, Moscow, Russia"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Platonov", 
        "givenName": "V. P.", 
        "id": "sg:person.012055230224.00", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012055230224.00"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Russian Academy of Sciences", 
          "id": "https://www.grid.ac/institutes/grid.4886.2", 
          "name": [
            "Scientific Research Institute for System Analysis, Russian Academy of Sciences, 117218, Moscow, Russia"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Zhgoon", 
        "givenName": "V. S.", 
        "id": "sg:person.014347152251.27", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014347152251.27"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Russian Academy of Sciences", 
          "id": "https://www.grid.ac/institutes/grid.4886.2", 
          "name": [
            "Scientific Research Institute for System Analysis, Russian Academy of Sciences, 117218, Moscow, Russia"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Petrunin", 
        "givenName": "M. M.", 
        "id": "sg:person.07522713411.98", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07522713411.98"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Russian Academy of Sciences", 
          "id": "https://www.grid.ac/institutes/grid.4886.2", 
          "name": [
            "Scientific Research Institute for System Analysis, Russian Academy of Sciences, 117218, Moscow, Russia"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Shteinikov", 
        "givenName": "Yu. N.", 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1134/s1064562415060034", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1026073428", 
          "https://doi.org/10.1134/s1064562415060034"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1134/s1064562416050148", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1041439271", 
          "https://doi.org/10.1134/s1064562416050148"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1134/s1064562416050148", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1041439271", 
          "https://doi.org/10.1134/s1064562416050148"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1515/crll.1826.1.185", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1043506193"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1070/rm2014v069n01abeh004877", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1058198433"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1070/rm9737", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1058198570"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1070/sm2009v200n11abeh004052", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1058202515"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1070/sm2009v200n11abeh004052", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1058202515"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1134/s1064562417030097", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1090675261", 
          "https://doi.org/10.1134/s1064562417030097"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1134/s106456241703019x", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1090682556", 
          "https://doi.org/10.1134/s106456241703019x"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1134/s1064562417040068", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1091493444", 
          "https://doi.org/10.1134/s1064562417040068"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1070/sm8998", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1100625525"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.4064/aa-95-2-139-166", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1101092748"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2018-11", 
    "datePublishedReg": "2018-11-01", 
    "description": "We prove the finiteness of the set of square-free polynomials f \u2208 k[x] of odd degree distinct from 11 considered up to a natural equivalence relation for which the continued fraction expansion of the irrationality f(x) in k((x)) is periodic and the corresponding hyperelliptic field k(x)(\u221af) contains an S-unit of degree 11. Moreover, it was proved for k = \u211a that there are no polynomials of odd degree distinct from 9 and 11 satisfying the conditions mentioned above.", 
    "genre": "research_article", 
    "id": "sg:pub.10.1134/s1064562418070281", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1136704", 
        "issn": [
          "1064-5624", 
          "1531-8362"
        ], 
        "name": "Doklady Mathematics", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "3", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "98"
      }
    ], 
    "name": "On the Finiteness of Hyperelliptic Fields with Special Properties and Periodic Expansion of \u221af", 
    "pagination": "641-645", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "19f59fda6b2a3811b6059ffbff883f8ff7255e7ecdc45202286d7856a348e28c"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1134/s1064562418070281"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1111224425"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1134/s1064562418070281", 
      "https://app.dimensions.ai/details/publication/pub.1111224425"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-11T08:36", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000314_0000000314/records_55826_00000000.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://link.springer.com/10.1134%2FS1064562418070281"
  }
]
 

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.10.1134/s1064562418070281'

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

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1134/s1064562418070281'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1134/s1064562418070281'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1134/s1064562418070281'


 

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

119 TRIPLES      21 PREDICATES      38 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1134/s1064562418070281 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author N5ab23627aaef48c1938768dfcafaec12
4 schema:citation sg:pub.10.1134/s1064562415060034
5 sg:pub.10.1134/s1064562416050148
6 sg:pub.10.1134/s1064562417030097
7 sg:pub.10.1134/s106456241703019x
8 sg:pub.10.1134/s1064562417040068
9 https://doi.org/10.1070/rm2014v069n01abeh004877
10 https://doi.org/10.1070/rm9737
11 https://doi.org/10.1070/sm2009v200n11abeh004052
12 https://doi.org/10.1070/sm8998
13 https://doi.org/10.1515/crll.1826.1.185
14 https://doi.org/10.4064/aa-95-2-139-166
15 schema:datePublished 2018-11
16 schema:datePublishedReg 2018-11-01
17 schema:description We prove the finiteness of the set of square-free polynomials f ∈ k[x] of odd degree distinct from 11 considered up to a natural equivalence relation for which the continued fraction expansion of the irrationality f(x) in k((x)) is periodic and the corresponding hyperelliptic field k(x)(√f) contains an S-unit of degree 11. Moreover, it was proved for k = ℚ that there are no polynomials of odd degree distinct from 9 and 11 satisfying the conditions mentioned above.
18 schema:genre research_article
19 schema:inLanguage en
20 schema:isAccessibleForFree false
21 schema:isPartOf N576de5cc8c1e401d9ea371648fdfe66b
22 N83a0950d9c70422b9eaca16bc8466939
23 sg:journal.1136704
24 schema:name On the Finiteness of Hyperelliptic Fields with Special Properties and Periodic Expansion of √f
25 schema:pagination 641-645
26 schema:productId N425f4531eb804ed8959ce440eeb60227
27 N7da290c938a84ea2a20201bfaf77ec73
28 Ne438df651eb64ecb992a05004f7cbb2a
29 schema:sameAs https://app.dimensions.ai/details/publication/pub.1111224425
30 https://doi.org/10.1134/s1064562418070281
31 schema:sdDatePublished 2019-04-11T08:36
32 schema:sdLicense https://scigraph.springernature.com/explorer/license/
33 schema:sdPublisher N2582973321ca492cbbdbee640d615f19
34 schema:url https://link.springer.com/10.1134%2FS1064562418070281
35 sgo:license sg:explorer/license/
36 sgo:sdDataset articles
37 rdf:type schema:ScholarlyArticle
38 N0a962d3c9a9b43a8b51210e547f922c6 schema:affiliation https://www.grid.ac/institutes/grid.4886.2
39 schema:familyName Shteinikov
40 schema:givenName Yu. N.
41 rdf:type schema:Person
42 N0d2d3ecce1b249528f0309f94dcb7bfe rdf:first N0a962d3c9a9b43a8b51210e547f922c6
43 rdf:rest rdf:nil
44 N114d12c2b1534ae094c907f720e6aa64 rdf:first sg:person.07522713411.98
45 rdf:rest N0d2d3ecce1b249528f0309f94dcb7bfe
46 N2582973321ca492cbbdbee640d615f19 schema:name Springer Nature - SN SciGraph project
47 rdf:type schema:Organization
48 N425f4531eb804ed8959ce440eeb60227 schema:name doi
49 schema:value 10.1134/s1064562418070281
50 rdf:type schema:PropertyValue
51 N576de5cc8c1e401d9ea371648fdfe66b schema:issueNumber 3
52 rdf:type schema:PublicationIssue
53 N5ab23627aaef48c1938768dfcafaec12 rdf:first sg:person.012055230224.00
54 rdf:rest Nc4f9cd718d73465da380452dd83c31b9
55 N7da290c938a84ea2a20201bfaf77ec73 schema:name dimensions_id
56 schema:value pub.1111224425
57 rdf:type schema:PropertyValue
58 N83a0950d9c70422b9eaca16bc8466939 schema:volumeNumber 98
59 rdf:type schema:PublicationVolume
60 Nc4f9cd718d73465da380452dd83c31b9 rdf:first sg:person.014347152251.27
61 rdf:rest N114d12c2b1534ae094c907f720e6aa64
62 Ne438df651eb64ecb992a05004f7cbb2a schema:name readcube_id
63 schema:value 19f59fda6b2a3811b6059ffbff883f8ff7255e7ecdc45202286d7856a348e28c
64 rdf:type schema:PropertyValue
65 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
66 schema:name Mathematical Sciences
67 rdf:type schema:DefinedTerm
68 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
69 schema:name Pure Mathematics
70 rdf:type schema:DefinedTerm
71 sg:journal.1136704 schema:issn 1064-5624
72 1531-8362
73 schema:name Doklady Mathematics
74 rdf:type schema:Periodical
75 sg:person.012055230224.00 schema:affiliation https://www.grid.ac/institutes/grid.4886.2
76 schema:familyName Platonov
77 schema:givenName V. P.
78 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012055230224.00
79 rdf:type schema:Person
80 sg:person.014347152251.27 schema:affiliation https://www.grid.ac/institutes/grid.4886.2
81 schema:familyName Zhgoon
82 schema:givenName V. S.
83 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014347152251.27
84 rdf:type schema:Person
85 sg:person.07522713411.98 schema:affiliation https://www.grid.ac/institutes/grid.4886.2
86 schema:familyName Petrunin
87 schema:givenName M. M.
88 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07522713411.98
89 rdf:type schema:Person
90 sg:pub.10.1134/s1064562415060034 schema:sameAs https://app.dimensions.ai/details/publication/pub.1026073428
91 https://doi.org/10.1134/s1064562415060034
92 rdf:type schema:CreativeWork
93 sg:pub.10.1134/s1064562416050148 schema:sameAs https://app.dimensions.ai/details/publication/pub.1041439271
94 https://doi.org/10.1134/s1064562416050148
95 rdf:type schema:CreativeWork
96 sg:pub.10.1134/s1064562417030097 schema:sameAs https://app.dimensions.ai/details/publication/pub.1090675261
97 https://doi.org/10.1134/s1064562417030097
98 rdf:type schema:CreativeWork
99 sg:pub.10.1134/s106456241703019x schema:sameAs https://app.dimensions.ai/details/publication/pub.1090682556
100 https://doi.org/10.1134/s106456241703019x
101 rdf:type schema:CreativeWork
102 sg:pub.10.1134/s1064562417040068 schema:sameAs https://app.dimensions.ai/details/publication/pub.1091493444
103 https://doi.org/10.1134/s1064562417040068
104 rdf:type schema:CreativeWork
105 https://doi.org/10.1070/rm2014v069n01abeh004877 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058198433
106 rdf:type schema:CreativeWork
107 https://doi.org/10.1070/rm9737 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058198570
108 rdf:type schema:CreativeWork
109 https://doi.org/10.1070/sm2009v200n11abeh004052 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058202515
110 rdf:type schema:CreativeWork
111 https://doi.org/10.1070/sm8998 schema:sameAs https://app.dimensions.ai/details/publication/pub.1100625525
112 rdf:type schema:CreativeWork
113 https://doi.org/10.1515/crll.1826.1.185 schema:sameAs https://app.dimensions.ai/details/publication/pub.1043506193
114 rdf:type schema:CreativeWork
115 https://doi.org/10.4064/aa-95-2-139-166 schema:sameAs https://app.dimensions.ai/details/publication/pub.1101092748
116 rdf:type schema:CreativeWork
117 https://www.grid.ac/institutes/grid.4886.2 schema:alternateName Russian Academy of Sciences
118 schema:name Scientific Research Institute for System Analysis, Russian Academy of Sciences, 117218, Moscow, Russia
119 rdf:type schema:Organization
 




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


...