Weak harmonic Maass forms of weight 5/2 and a mock modular form for the partition function View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2015-12

AUTHORS

Scott Ahlgren, Nickolas Andersen

ABSTRACT

We construct a natural basis for the space of weak harmonic Maass forms of weight 5/2 on the full modular group. The nonholomorphic part of the first element of this basis encodes the values of the ordinary partition function p(n). We obtain a formula for the coefficients of the mock modular forms of weight 5/2 in terms of regularized inner products of weakly holomorphic modular forms of weight −1/2, and we obtain Hecke-type relations among these mock modular forms. More... »

PAGES

10

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s40993-015-0011-9

DOI

http://dx.doi.org/10.1007/s40993-015-0011-9

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1013973243


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": {
          "name": [
            "Department of Mathematics, University of Illinois, Urbana IL, USA"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Ahlgren", 
        "givenName": "Scott", 
        "id": "sg:person.01232330064.48", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01232330064.48"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "name": [
            "Department of Mathematics, University of Illinois, Urbana IL, USA"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Andersen", 
        "givenName": "Nickolas", 
        "id": "sg:person.015327000641.67", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015327000641.67"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1007/bfb0061302", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1005230007", 
          "https://doi.org/10.1007/bfb0061302"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bfb0061302", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1005230007", 
          "https://doi.org/10.1007/bfb0061302"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1112/plms/s2-43.4.241", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1009388005"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s11139-013-9544-5", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1010561651", 
          "https://doi.org/10.1007/s11139-013-9544-5"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s00208-005-0723-6", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1013002616", 
          "https://doi.org/10.1007/s00208-005-0723-6"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1112/blms/bdr072", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1017545500"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1515/forum-2012-0011", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1019015253"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.jnt.2013.01.011", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1022433624"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s00209-008-0460-0", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1023862341", 
          "https://doi.org/10.1007/s00209-008-0460-0"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s00209-008-0460-0", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1023862341", 
          "https://doi.org/10.1007/s00209-008-0460-0"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.aim.2013.05.028", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1027794400"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.aim.2012.09.025", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1030215212"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s002220050232", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1032505399", 
          "https://doi.org/10.1007/s002220050232"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s00222-005-0493-5", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1040824251", 
          "https://doi.org/10.1007/s00222-005-0493-5"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s00222-005-0493-5", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1040824251", 
          "https://doi.org/10.1007/s00222-005-0493-5"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1093/imrn/rnq159", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1059690725"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1093/imrn/rnq159", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1059690725"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1215/s0012-7094-04-12513-8", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1064415475"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.4007/annals.2010.172.2135", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1071867270"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.4007/annals.2010.172.2135", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1071867270"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.4007/annals.2011.173.2.8", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1071867322"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.4310/cdm.2008.v2008.n1.a5", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1072458298"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.4310/mrl.2009.v16.n1.a7", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1072462699"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://app.dimensions.ai/details/publication/pub.1086032748", 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://app.dimensions.ai/details/publication/pub.1086032748", 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1090/gsm/017", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1098740272"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2015-12", 
    "datePublishedReg": "2015-12-01", 
    "description": "We construct a natural basis for the space of weak harmonic Maass forms of weight 5/2 on the full modular group. The nonholomorphic part of the first element of this basis encodes the values of the ordinary partition function p(n). We obtain a formula for the coefficients of the mock modular forms of weight 5/2 in terms of regularized inner products of weakly holomorphic modular forms of weight \u22121/2, and we obtain Hecke-type relations among these mock modular forms.", 
    "genre": "research_article", 
    "id": "sg:pub.10.1007/s40993-015-0011-9", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": true, 
    "isPartOf": [
      {
        "id": "sg:journal.1053185", 
        "issn": [
          "2522-0160", 
          "2363-9555"
        ], 
        "name": "Research in Number Theory", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "1", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "1"
      }
    ], 
    "name": "Weak harmonic Maass forms of weight 5/2 and a mock modular form for the partition function", 
    "pagination": "10", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "42908047ef17569c6ee58e895f49f51baae7d6eab0515f7584beff70e0edbb89"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s40993-015-0011-9"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1013973243"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s40993-015-0011-9", 
      "https://app.dimensions.ai/details/publication/pub.1013973243"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-11T09:55", 
    "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/v90/0000000347_0000000347/records_89801_00000000.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "http://link.springer.com/10.1007%2Fs40993-015-0011-9"
  }
]
 

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/s40993-015-0011-9'

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/s40993-015-0011-9'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s40993-015-0011-9'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s40993-015-0011-9'


 

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

134 TRIPLES      21 PREDICATES      47 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s40993-015-0011-9 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author Nbbc7c61b9f9f49a38430cf66a5b5a2f4
4 schema:citation sg:pub.10.1007/bfb0061302
5 sg:pub.10.1007/s00208-005-0723-6
6 sg:pub.10.1007/s00209-008-0460-0
7 sg:pub.10.1007/s00222-005-0493-5
8 sg:pub.10.1007/s002220050232
9 sg:pub.10.1007/s11139-013-9544-5
10 https://app.dimensions.ai/details/publication/pub.1086032748
11 https://doi.org/10.1016/j.aim.2012.09.025
12 https://doi.org/10.1016/j.aim.2013.05.028
13 https://doi.org/10.1016/j.jnt.2013.01.011
14 https://doi.org/10.1090/gsm/017
15 https://doi.org/10.1093/imrn/rnq159
16 https://doi.org/10.1112/blms/bdr072
17 https://doi.org/10.1112/plms/s2-43.4.241
18 https://doi.org/10.1215/s0012-7094-04-12513-8
19 https://doi.org/10.1515/forum-2012-0011
20 https://doi.org/10.4007/annals.2010.172.2135
21 https://doi.org/10.4007/annals.2011.173.2.8
22 https://doi.org/10.4310/cdm.2008.v2008.n1.a5
23 https://doi.org/10.4310/mrl.2009.v16.n1.a7
24 schema:datePublished 2015-12
25 schema:datePublishedReg 2015-12-01
26 schema:description We construct a natural basis for the space of weak harmonic Maass forms of weight 5/2 on the full modular group. The nonholomorphic part of the first element of this basis encodes the values of the ordinary partition function p(n). We obtain a formula for the coefficients of the mock modular forms of weight 5/2 in terms of regularized inner products of weakly holomorphic modular forms of weight −1/2, and we obtain Hecke-type relations among these mock modular forms.
27 schema:genre research_article
28 schema:inLanguage en
29 schema:isAccessibleForFree true
30 schema:isPartOf N04f23c2d9c63437db4b88e843a696782
31 Nf4498364feac4a318602b6eb1eb547f4
32 sg:journal.1053185
33 schema:name Weak harmonic Maass forms of weight 5/2 and a mock modular form for the partition function
34 schema:pagination 10
35 schema:productId N2123aed650374b03bddc799b6da466fc
36 N262c8c03a9ce4e80b99ff355aed88d29
37 N6b36525160a04484bf96ba2b48d902e7
38 schema:sameAs https://app.dimensions.ai/details/publication/pub.1013973243
39 https://doi.org/10.1007/s40993-015-0011-9
40 schema:sdDatePublished 2019-04-11T09:55
41 schema:sdLicense https://scigraph.springernature.com/explorer/license/
42 schema:sdPublisher N96036296608f47d7a23e2b8918fa2383
43 schema:url http://link.springer.com/10.1007%2Fs40993-015-0011-9
44 sgo:license sg:explorer/license/
45 sgo:sdDataset articles
46 rdf:type schema:ScholarlyArticle
47 N01c9739f9e8c4e99a457b2113e135468 rdf:first sg:person.015327000641.67
48 rdf:rest rdf:nil
49 N04f23c2d9c63437db4b88e843a696782 schema:issueNumber 1
50 rdf:type schema:PublicationIssue
51 N2123aed650374b03bddc799b6da466fc schema:name doi
52 schema:value 10.1007/s40993-015-0011-9
53 rdf:type schema:PropertyValue
54 N262c8c03a9ce4e80b99ff355aed88d29 schema:name dimensions_id
55 schema:value pub.1013973243
56 rdf:type schema:PropertyValue
57 N6b36525160a04484bf96ba2b48d902e7 schema:name readcube_id
58 schema:value 42908047ef17569c6ee58e895f49f51baae7d6eab0515f7584beff70e0edbb89
59 rdf:type schema:PropertyValue
60 N6f06bb4988264825ae60605f633d9a8c schema:name Department of Mathematics, University of Illinois, Urbana IL, USA
61 rdf:type schema:Organization
62 N777ec9d4015d422fb7f4224c931476f2 schema:name Department of Mathematics, University of Illinois, Urbana IL, USA
63 rdf:type schema:Organization
64 N96036296608f47d7a23e2b8918fa2383 schema:name Springer Nature - SN SciGraph project
65 rdf:type schema:Organization
66 Nbbc7c61b9f9f49a38430cf66a5b5a2f4 rdf:first sg:person.01232330064.48
67 rdf:rest N01c9739f9e8c4e99a457b2113e135468
68 Nf4498364feac4a318602b6eb1eb547f4 schema:volumeNumber 1
69 rdf:type schema:PublicationVolume
70 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
71 schema:name Mathematical Sciences
72 rdf:type schema:DefinedTerm
73 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
74 schema:name Pure Mathematics
75 rdf:type schema:DefinedTerm
76 sg:journal.1053185 schema:issn 2363-9555
77 2522-0160
78 schema:name Research in Number Theory
79 rdf:type schema:Periodical
80 sg:person.01232330064.48 schema:affiliation N6f06bb4988264825ae60605f633d9a8c
81 schema:familyName Ahlgren
82 schema:givenName Scott
83 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01232330064.48
84 rdf:type schema:Person
85 sg:person.015327000641.67 schema:affiliation N777ec9d4015d422fb7f4224c931476f2
86 schema:familyName Andersen
87 schema:givenName Nickolas
88 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015327000641.67
89 rdf:type schema:Person
90 sg:pub.10.1007/bfb0061302 schema:sameAs https://app.dimensions.ai/details/publication/pub.1005230007
91 https://doi.org/10.1007/bfb0061302
92 rdf:type schema:CreativeWork
93 sg:pub.10.1007/s00208-005-0723-6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1013002616
94 https://doi.org/10.1007/s00208-005-0723-6
95 rdf:type schema:CreativeWork
96 sg:pub.10.1007/s00209-008-0460-0 schema:sameAs https://app.dimensions.ai/details/publication/pub.1023862341
97 https://doi.org/10.1007/s00209-008-0460-0
98 rdf:type schema:CreativeWork
99 sg:pub.10.1007/s00222-005-0493-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1040824251
100 https://doi.org/10.1007/s00222-005-0493-5
101 rdf:type schema:CreativeWork
102 sg:pub.10.1007/s002220050232 schema:sameAs https://app.dimensions.ai/details/publication/pub.1032505399
103 https://doi.org/10.1007/s002220050232
104 rdf:type schema:CreativeWork
105 sg:pub.10.1007/s11139-013-9544-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1010561651
106 https://doi.org/10.1007/s11139-013-9544-5
107 rdf:type schema:CreativeWork
108 https://app.dimensions.ai/details/publication/pub.1086032748 schema:CreativeWork
109 https://doi.org/10.1016/j.aim.2012.09.025 schema:sameAs https://app.dimensions.ai/details/publication/pub.1030215212
110 rdf:type schema:CreativeWork
111 https://doi.org/10.1016/j.aim.2013.05.028 schema:sameAs https://app.dimensions.ai/details/publication/pub.1027794400
112 rdf:type schema:CreativeWork
113 https://doi.org/10.1016/j.jnt.2013.01.011 schema:sameAs https://app.dimensions.ai/details/publication/pub.1022433624
114 rdf:type schema:CreativeWork
115 https://doi.org/10.1090/gsm/017 schema:sameAs https://app.dimensions.ai/details/publication/pub.1098740272
116 rdf:type schema:CreativeWork
117 https://doi.org/10.1093/imrn/rnq159 schema:sameAs https://app.dimensions.ai/details/publication/pub.1059690725
118 rdf:type schema:CreativeWork
119 https://doi.org/10.1112/blms/bdr072 schema:sameAs https://app.dimensions.ai/details/publication/pub.1017545500
120 rdf:type schema:CreativeWork
121 https://doi.org/10.1112/plms/s2-43.4.241 schema:sameAs https://app.dimensions.ai/details/publication/pub.1009388005
122 rdf:type schema:CreativeWork
123 https://doi.org/10.1215/s0012-7094-04-12513-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064415475
124 rdf:type schema:CreativeWork
125 https://doi.org/10.1515/forum-2012-0011 schema:sameAs https://app.dimensions.ai/details/publication/pub.1019015253
126 rdf:type schema:CreativeWork
127 https://doi.org/10.4007/annals.2010.172.2135 schema:sameAs https://app.dimensions.ai/details/publication/pub.1071867270
128 rdf:type schema:CreativeWork
129 https://doi.org/10.4007/annals.2011.173.2.8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1071867322
130 rdf:type schema:CreativeWork
131 https://doi.org/10.4310/cdm.2008.v2008.n1.a5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1072458298
132 rdf:type schema:CreativeWork
133 https://doi.org/10.4310/mrl.2009.v16.n1.a7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1072462699
134 rdf:type schema:CreativeWork
 




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


...