Equidistribution of Heegner points and the partition function View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2010-01-20

AUTHORS

Amanda Folsom, Riad Masri

ABSTRACT

Let p(n) denote the number of partitions of a positive integer n. In this paper we study the asymptotic growth of p(n) using the equidistribution of Galois orbits of Heegner points on the modular curve X0(6). We obtain a new asymptotic formula for p(n) with an effective error term which is \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${O(n^{-(\frac{1}{2}+\delta)})}$$\end{document} for some δ > 0. We then use this asymptotic formula to sharpen the classical bounds of Hardy and Ramanujan, Rademacher, and Lehmer on the error term in Rademacher’s exact formula for p(n). More... »

PAGES

289-317

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00208-010-0478-6

DOI

http://dx.doi.org/10.1007/s00208-010-0478-6

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1046269669


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 Wisconsin, 53706, Madison, WI, USA", 
          "id": "http://www.grid.ac/institutes/grid.14003.36", 
          "name": [
            "Department of Mathematics, University of Wisconsin, 53706, Madison, WI, USA"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Folsom", 
        "givenName": "Amanda", 
        "id": "sg:person.014433460651.03", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014433460651.03"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Department of Mathematics, University of Wisconsin, 53706, Madison, WI, USA", 
          "id": "http://www.grid.ac/institutes/grid.14003.36", 
          "name": [
            "Department of Mathematics, University of Wisconsin, 53706, Madison, WI, USA"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Masri", 
        "givenName": "Riad", 
        "id": "sg:person.0717644044.71", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0717644044.71"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1007/s00222-005-0468-6", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1050953835", 
          "https://doi.org/10.1007/s00222-005-0468-6"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01388809", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1039451295", 
          "https://doi.org/10.1007/bf01388809"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01393993", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1049841809", 
          "https://doi.org/10.1007/bf01393993"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-642-80615-5", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1049342383", 
          "https://doi.org/10.1007/978-3-642-80615-5"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01458081", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1026477938", 
          "https://doi.org/10.1007/bf01458081"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s00208-005-0706-7", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1052775798", 
          "https://doi.org/10.1007/s00208-005-0706-7"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2010-01-20", 
    "datePublishedReg": "2010-01-20", 
    "description": "Let p(n) denote the number of partitions of a positive integer n. In this paper we study the asymptotic growth of p(n) using the equidistribution of Galois orbits of Heegner points on the modular curve X0(6). We obtain a new asymptotic formula for p(n) with an effective error term which is \\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$${O(n^{-(\\frac{1}{2}+\\delta)})}$$\\end{document} for some \u03b4\u00a0> 0. We then use this asymptotic formula to sharpen the classical bounds of Hardy and Ramanujan, Rademacher, and Lehmer on the error term in Rademacher\u2019s exact formula for p(n).", 
    "genre": "article", 
    "id": "sg:pub.10.1007/s00208-010-0478-6", 
    "inLanguage": "en", 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1120885", 
        "issn": [
          "0025-5831", 
          "1432-1807"
        ], 
        "name": "Mathematische Annalen", 
        "publisher": "Springer Nature", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "2", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "348"
      }
    ], 
    "keywords": [
      "function", 
      "number", 
      "growth", 
      "curves", 
      "terms", 
      "formula", 
      "orbit", 
      "Hardy", 
      "n.", 
      "positive integer n.", 
      "partition", 
      "integer n.", 
      "paper", 
      "asymptotic growth", 
      "Lehmer", 
      "error term", 
      "Ramanujan", 
      "number of partitions", 
      "modular curves", 
      "asymptotic formula", 
      "Rademacher", 
      "new asymptotic formula", 
      "equidistribution", 
      "exact formula", 
      "bounds", 
      "classical bounds", 
      "Galois orbits", 
      "Heegner", 
      "partition function", 
      "effective error term", 
      "Rademacher\u2019s exact formula", 
      "Equidistribution of Heegner"
    ], 
    "name": "Equidistribution of Heegner points and the partition function", 
    "pagination": "289-317", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1046269669"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s00208-010-0478-6"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s00208-010-0478-6", 
      "https://app.dimensions.ai/details/publication/pub.1046269669"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2021-12-01T19:24", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-springernature-scigraph/baseset/20211201/entities/gbq_results/article/article_526.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://doi.org/10.1007/s00208-010-0478-6"
  }
]
 

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/s00208-010-0478-6'

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/s00208-010-0478-6'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s00208-010-0478-6'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s00208-010-0478-6'


 

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

121 TRIPLES      22 PREDICATES      63 URIs      49 LITERALS      6 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s00208-010-0478-6 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author N7a798f754b9242899b3b03a6abd297dd
4 schema:citation sg:pub.10.1007/978-3-642-80615-5
5 sg:pub.10.1007/bf01388809
6 sg:pub.10.1007/bf01393993
7 sg:pub.10.1007/bf01458081
8 sg:pub.10.1007/s00208-005-0706-7
9 sg:pub.10.1007/s00222-005-0468-6
10 schema:datePublished 2010-01-20
11 schema:datePublishedReg 2010-01-20
12 schema:description Let p(n) denote the number of partitions of a positive integer n. In this paper we study the asymptotic growth of p(n) using the equidistribution of Galois orbits of Heegner points on the modular curve X0(6). We obtain a new asymptotic formula for p(n) with an effective error term which is \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${O(n^{-(\frac{1}{2}+\delta)})}$$\end{document} for some δ > 0. We then use this asymptotic formula to sharpen the classical bounds of Hardy and Ramanujan, Rademacher, and Lehmer on the error term in Rademacher’s exact formula for p(n).
13 schema:genre article
14 schema:inLanguage en
15 schema:isAccessibleForFree false
16 schema:isPartOf N210a09c9078a47f2bf7160ea28dda46d
17 N7b7a716490f14f649cb5b6220d743821
18 sg:journal.1120885
19 schema:keywords Equidistribution of Heegner
20 Galois orbits
21 Hardy
22 Heegner
23 Lehmer
24 Rademacher
25 Rademacher’s exact formula
26 Ramanujan
27 asymptotic formula
28 asymptotic growth
29 bounds
30 classical bounds
31 curves
32 effective error term
33 equidistribution
34 error term
35 exact formula
36 formula
37 function
38 growth
39 integer n.
40 modular curves
41 n.
42 new asymptotic formula
43 number
44 number of partitions
45 orbit
46 paper
47 partition
48 partition function
49 positive integer n.
50 terms
51 schema:name Equidistribution of Heegner points and the partition function
52 schema:pagination 289-317
53 schema:productId N42c3a1fbcccb4a5494dded8bb3959807
54 Nfde7499d38294323861fd08ce900d36f
55 schema:sameAs https://app.dimensions.ai/details/publication/pub.1046269669
56 https://doi.org/10.1007/s00208-010-0478-6
57 schema:sdDatePublished 2021-12-01T19:24
58 schema:sdLicense https://scigraph.springernature.com/explorer/license/
59 schema:sdPublisher N05d51938fd924f0b89934e317f35bfec
60 schema:url https://doi.org/10.1007/s00208-010-0478-6
61 sgo:license sg:explorer/license/
62 sgo:sdDataset articles
63 rdf:type schema:ScholarlyArticle
64 N05d51938fd924f0b89934e317f35bfec schema:name Springer Nature - SN SciGraph project
65 rdf:type schema:Organization
66 N1d4242f0d7424ab5b2370f3b25db600d rdf:first sg:person.0717644044.71
67 rdf:rest rdf:nil
68 N210a09c9078a47f2bf7160ea28dda46d schema:issueNumber 2
69 rdf:type schema:PublicationIssue
70 N42c3a1fbcccb4a5494dded8bb3959807 schema:name doi
71 schema:value 10.1007/s00208-010-0478-6
72 rdf:type schema:PropertyValue
73 N7a798f754b9242899b3b03a6abd297dd rdf:first sg:person.014433460651.03
74 rdf:rest N1d4242f0d7424ab5b2370f3b25db600d
75 N7b7a716490f14f649cb5b6220d743821 schema:volumeNumber 348
76 rdf:type schema:PublicationVolume
77 Nfde7499d38294323861fd08ce900d36f schema:name dimensions_id
78 schema:value pub.1046269669
79 rdf:type schema:PropertyValue
80 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
81 schema:name Mathematical Sciences
82 rdf:type schema:DefinedTerm
83 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
84 schema:name Pure Mathematics
85 rdf:type schema:DefinedTerm
86 sg:journal.1120885 schema:issn 0025-5831
87 1432-1807
88 schema:name Mathematische Annalen
89 schema:publisher Springer Nature
90 rdf:type schema:Periodical
91 sg:person.014433460651.03 schema:affiliation grid-institutes:grid.14003.36
92 schema:familyName Folsom
93 schema:givenName Amanda
94 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014433460651.03
95 rdf:type schema:Person
96 sg:person.0717644044.71 schema:affiliation grid-institutes:grid.14003.36
97 schema:familyName Masri
98 schema:givenName Riad
99 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0717644044.71
100 rdf:type schema:Person
101 sg:pub.10.1007/978-3-642-80615-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1049342383
102 https://doi.org/10.1007/978-3-642-80615-5
103 rdf:type schema:CreativeWork
104 sg:pub.10.1007/bf01388809 schema:sameAs https://app.dimensions.ai/details/publication/pub.1039451295
105 https://doi.org/10.1007/bf01388809
106 rdf:type schema:CreativeWork
107 sg:pub.10.1007/bf01393993 schema:sameAs https://app.dimensions.ai/details/publication/pub.1049841809
108 https://doi.org/10.1007/bf01393993
109 rdf:type schema:CreativeWork
110 sg:pub.10.1007/bf01458081 schema:sameAs https://app.dimensions.ai/details/publication/pub.1026477938
111 https://doi.org/10.1007/bf01458081
112 rdf:type schema:CreativeWork
113 sg:pub.10.1007/s00208-005-0706-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1052775798
114 https://doi.org/10.1007/s00208-005-0706-7
115 rdf:type schema:CreativeWork
116 sg:pub.10.1007/s00222-005-0468-6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1050953835
117 https://doi.org/10.1007/s00222-005-0468-6
118 rdf:type schema:CreativeWork
119 grid-institutes:grid.14003.36 schema:alternateName Department of Mathematics, University of Wisconsin, 53706, Madison, WI, USA
120 schema:name Department of Mathematics, University of Wisconsin, 53706, Madison, WI, USA
121 rdf:type schema:Organization
 




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


...