Almost Uniform Distribution Modulo 1 and the Distribution of Primes View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1998-01

AUTHORS

S. Akiyama

ABSTRACT

Let (an), n = 1, 2, ... be a sequence of real numbers which is related with number theoretic functions such as Pn, the n-th prime. We study the distribution of the fractional parts of (an) using the concept of "almost uniform distribution" defined in [9]. Then we can show a generalization of the results of [2] on the convex property of log Pn. The method may be extended as well to other oscillation problems of number theoretical interest. More... »

PAGES

39-44

Identifiers

URI

http://scigraph.springernature.com/pub.10.1023/a:1006514302520

DOI

http://dx.doi.org/10.1023/a:1006514302520

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1028622937


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": "Faculty of Science Niigata University Niigata, 950-21, Japan", 
          "id": "http://www.grid.ac/institutes/grid.260975.f", 
          "name": [
            "Faculty of Science Niigata University Niigata, 950-21, Japan"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Akiyama", 
        "givenName": "S.", 
        "id": "sg:person.011153327405.03", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011153327405.03"
        ], 
        "type": "Person"
      }
    ], 
    "datePublished": "1998-01", 
    "datePublishedReg": "1998-01-01", 
    "description": "Let (an), n = 1, 2, ... be a sequence of real numbers which is related with number theoretic functions such as Pn, the n-th prime. We study the distribution of the fractional parts of (an) using the concept of \"almost uniform distribution\" defined in [9]. Then we can show a generalization of the results of [2] on the convex property of log Pn. The method may be extended as well to other oscillation problems of number theoretical interest.", 
    "genre": "article", 
    "id": "sg:pub.10.1023/a:1006514302520", 
    "inLanguage": "en", 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1136684", 
        "issn": [
          "0236-5294", 
          "1588-2632"
        ], 
        "name": "Acta Mathematica Hungarica", 
        "publisher": "Springer Nature", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "1-2", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "78"
      }
    ], 
    "keywords": [
      "n-th prime", 
      "uniform distribution modulo 1", 
      "number-theoretic functions", 
      "distribution of primes", 
      "distribution modulo 1", 
      "convex properties", 
      "oscillation problem", 
      "theoretic functions", 
      "real numbers", 
      "theoretical interest", 
      "modulo 1", 
      "fractional part", 
      "uniform distribution", 
      "generalization", 
      "distribution", 
      "primes", 
      "problem", 
      "PN", 
      "properties", 
      "function", 
      "number", 
      "concept", 
      "results", 
      "interest", 
      "sequence", 
      "part", 
      "method"
    ], 
    "name": "Almost Uniform Distribution Modulo 1 and the Distribution of Primes", 
    "pagination": "39-44", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1028622937"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1023/a:1006514302520"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1023/a:1006514302520", 
      "https://app.dimensions.ai/details/publication/pub.1028622937"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2022-05-10T09:48", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-springernature-scigraph/baseset/20220509/entities/gbq_results/article/article_278.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://doi.org/10.1023/a:1006514302520"
  }
]
 

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.10.1023/a:1006514302520'

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

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1023/a:1006514302520'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1023/a:1006514302520'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1023/a:1006514302520'


 

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

85 TRIPLES      21 PREDICATES      53 URIs      45 LITERALS      6 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1023/a:1006514302520 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author Nbee5aa6c79be4e948eddda049465d0dd
4 schema:datePublished 1998-01
5 schema:datePublishedReg 1998-01-01
6 schema:description Let (an), n = 1, 2, ... be a sequence of real numbers which is related with number theoretic functions such as Pn, the n-th prime. We study the distribution of the fractional parts of (an) using the concept of "almost uniform distribution" defined in [9]. Then we can show a generalization of the results of [2] on the convex property of log Pn. The method may be extended as well to other oscillation problems of number theoretical interest.
7 schema:genre article
8 schema:inLanguage en
9 schema:isAccessibleForFree false
10 schema:isPartOf N8fb2a2cb0dda411ca76128e2247b9476
11 Nda918b30524f4807b173b324b88afbb0
12 sg:journal.1136684
13 schema:keywords PN
14 concept
15 convex properties
16 distribution
17 distribution modulo 1
18 distribution of primes
19 fractional part
20 function
21 generalization
22 interest
23 method
24 modulo 1
25 n-th prime
26 number
27 number-theoretic functions
28 oscillation problem
29 part
30 primes
31 problem
32 properties
33 real numbers
34 results
35 sequence
36 theoretic functions
37 theoretical interest
38 uniform distribution
39 uniform distribution modulo 1
40 schema:name Almost Uniform Distribution Modulo 1 and the Distribution of Primes
41 schema:pagination 39-44
42 schema:productId N2d38be6c7ff94c03a36eee86a4a2f9d8
43 Ne5e4c36af7c84ef3bb54bd2c9f676588
44 schema:sameAs https://app.dimensions.ai/details/publication/pub.1028622937
45 https://doi.org/10.1023/a:1006514302520
46 schema:sdDatePublished 2022-05-10T09:48
47 schema:sdLicense https://scigraph.springernature.com/explorer/license/
48 schema:sdPublisher N7f799dc38c9d446ca16d12bbe9369606
49 schema:url https://doi.org/10.1023/a:1006514302520
50 sgo:license sg:explorer/license/
51 sgo:sdDataset articles
52 rdf:type schema:ScholarlyArticle
53 N2d38be6c7ff94c03a36eee86a4a2f9d8 schema:name doi
54 schema:value 10.1023/a:1006514302520
55 rdf:type schema:PropertyValue
56 N7f799dc38c9d446ca16d12bbe9369606 schema:name Springer Nature - SN SciGraph project
57 rdf:type schema:Organization
58 N8fb2a2cb0dda411ca76128e2247b9476 schema:issueNumber 1-2
59 rdf:type schema:PublicationIssue
60 Nbee5aa6c79be4e948eddda049465d0dd rdf:first sg:person.011153327405.03
61 rdf:rest rdf:nil
62 Nda918b30524f4807b173b324b88afbb0 schema:volumeNumber 78
63 rdf:type schema:PublicationVolume
64 Ne5e4c36af7c84ef3bb54bd2c9f676588 schema:name dimensions_id
65 schema:value pub.1028622937
66 rdf:type schema:PropertyValue
67 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
68 schema:name Mathematical Sciences
69 rdf:type schema:DefinedTerm
70 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
71 schema:name Pure Mathematics
72 rdf:type schema:DefinedTerm
73 sg:journal.1136684 schema:issn 0236-5294
74 1588-2632
75 schema:name Acta Mathematica Hungarica
76 schema:publisher Springer Nature
77 rdf:type schema:Periodical
78 sg:person.011153327405.03 schema:affiliation grid-institutes:grid.260975.f
79 schema:familyName Akiyama
80 schema:givenName S.
81 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011153327405.03
82 rdf:type schema:Person
83 grid-institutes:grid.260975.f schema:alternateName Faculty of Science Niigata University Niigata, 950-21, Japan
84 schema:name Faculty of Science Niigata University Niigata, 950-21, Japan
85 rdf:type schema:Organization
 




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


...