Revisiting Rademacher's Formula for the Partition Function p(n View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2000-12

AUTHORS

Wladimir De Azevedo Pribitkin

ABSTRACT

We provide a new proof of Rademacher's celebrated exact formula for the partition function. Along the way we present a simple treatment of an integral which is ubiquitous in the theory of nonanalytic automorphic forms.

PAGES

455-467

References to SciGraph publications

  • 1982-06. Kloosterman sums and Fourier coefficients of cusp forms in INVENTIONES MATHEMATICAE
  • 1955-12. Die Funktionalgleichungen einiger Dirichletscher Reihen in MATHEMATISCHE ZEITSCHRIFT
  • 1986-02. On the Fourier coefficients of small positive powers of θ (τ) in INVENTIONES MATHEMATICAE
  • Journal

    TITLE

    The Ramanujan Journal

    ISSUE

    4

    VOLUME

    4

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1023/a:1009828302300

    DOI

    http://dx.doi.org/10.1023/a:1009828302300

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1036348786


    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", 
        "author": [
          {
            "affiliation": {
              "alternateName": "Princeton University", 
              "id": "https://www.grid.ac/institutes/grid.16750.35", 
              "name": [
                "Department of Mathematics, Princeton University, 607 Fine Hall, Washington Road, 08544-1000, Princeton, New Jersey"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Pribitkin", 
            "givenName": "Wladimir De Azevedo", 
            "id": "sg:person.07704611215.01", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07704611215.01"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "https://doi.org/10.1112/plms/s2-17.1.75", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1009143639"
            ], 
            "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/bf01187948", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1012764582", 
              "https://doi.org/10.1007/bf01187948"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01388796", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1023784435", 
              "https://doi.org/10.1007/bf01388796"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1515/crll.1967.227.86", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1025554343"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1090/s0002-9947-1974-0344196-8", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1028240869"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1073/pnas.23.2.78", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1038275601"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf01390728", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1044380812", 
              "https://doi.org/10.1007/bf01390728"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1515/crll.1877.83.265", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1049127938"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1070/sm1981v039n03abeh001518", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1058199930"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.2307/1968973", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1069674378"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.2307/1971381", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1069676654"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1090/pspum/049.2/1013169", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1089196869"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.4064/aa-91-4-291-309", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1092041515"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.4064/aa-93-4-343-358", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1101092722"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2000-12", 
        "datePublishedReg": "2000-12-01", 
        "description": "We provide a new proof of Rademacher's celebrated exact formula for the partition function. Along the way we present a simple treatment of an integral which is ubiquitous in the theory of nonanalytic automorphic forms.", 
        "genre": "research_article", 
        "id": "sg:pub.10.1023/a:1009828302300", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": false, 
        "isPartOf": [
          {
            "id": "sg:journal.1136382", 
            "issn": [
              "1382-4090", 
              "1572-9303"
            ], 
            "name": "The Ramanujan Journal", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "4", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "4"
          }
        ], 
        "name": "Revisiting Rademacher's Formula for the Partition Function p(n", 
        "pagination": "455-467", 
        "productId": [
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "ad26bc473eb54309c98459f0bd6c324328b6a99687624d634b780e9026dab4bf"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1023/a:1009828302300"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1036348786"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1023/a:1009828302300", 
          "https://app.dimensions.ai/details/publication/pub.1036348786"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2019-04-10T23:21", 
        "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/v90/0000000001_0000000264/records_8693_00000500.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "http://link.springer.com/10.1023/A:1009828302300"
      }
    ]
     

    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:1009828302300'

    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:1009828302300'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1023/a:1009828302300'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1023/a:1009828302300'


     

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

    101 TRIPLES      20 PREDICATES      40 URIs      19 LITERALS      7 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1023/a:1009828302300 schema:author N26f01ed1d1f64c81a70a5f48fd2fa15c
    2 schema:citation sg:pub.10.1007/bf01187948
    3 sg:pub.10.1007/bf01388796
    4 sg:pub.10.1007/bf01390728
    5 https://doi.org/10.1070/sm1981v039n03abeh001518
    6 https://doi.org/10.1073/pnas.23.2.78
    7 https://doi.org/10.1090/pspum/049.2/1013169
    8 https://doi.org/10.1090/s0002-9947-1974-0344196-8
    9 https://doi.org/10.1112/plms/s2-17.1.75
    10 https://doi.org/10.1112/plms/s2-43.4.241
    11 https://doi.org/10.1515/crll.1877.83.265
    12 https://doi.org/10.1515/crll.1967.227.86
    13 https://doi.org/10.2307/1968973
    14 https://doi.org/10.2307/1971381
    15 https://doi.org/10.4064/aa-91-4-291-309
    16 https://doi.org/10.4064/aa-93-4-343-358
    17 schema:datePublished 2000-12
    18 schema:datePublishedReg 2000-12-01
    19 schema:description We provide a new proof of Rademacher's celebrated exact formula for the partition function. Along the way we present a simple treatment of an integral which is ubiquitous in the theory of nonanalytic automorphic forms.
    20 schema:genre research_article
    21 schema:inLanguage en
    22 schema:isAccessibleForFree false
    23 schema:isPartOf N20114d8e67f842848373d67ad4dbfa56
    24 N8a3a64270de247c28e876767d992fd8c
    25 sg:journal.1136382
    26 schema:name Revisiting Rademacher's Formula for the Partition Function p(n
    27 schema:pagination 455-467
    28 schema:productId N00802cb050ee4ca993e45edc238da452
    29 N6d134a6f1ad04a0bacf0a9cea347997a
    30 Nd9cbf5224a0f4ccc85061fffc135092c
    31 schema:sameAs https://app.dimensions.ai/details/publication/pub.1036348786
    32 https://doi.org/10.1023/a:1009828302300
    33 schema:sdDatePublished 2019-04-10T23:21
    34 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    35 schema:sdPublisher Nc200db170ed149c3a2468a066ee9d13a
    36 schema:url http://link.springer.com/10.1023/A:1009828302300
    37 sgo:license sg:explorer/license/
    38 sgo:sdDataset articles
    39 rdf:type schema:ScholarlyArticle
    40 N00802cb050ee4ca993e45edc238da452 schema:name doi
    41 schema:value 10.1023/a:1009828302300
    42 rdf:type schema:PropertyValue
    43 N20114d8e67f842848373d67ad4dbfa56 schema:issueNumber 4
    44 rdf:type schema:PublicationIssue
    45 N26f01ed1d1f64c81a70a5f48fd2fa15c rdf:first sg:person.07704611215.01
    46 rdf:rest rdf:nil
    47 N6d134a6f1ad04a0bacf0a9cea347997a schema:name dimensions_id
    48 schema:value pub.1036348786
    49 rdf:type schema:PropertyValue
    50 N8a3a64270de247c28e876767d992fd8c schema:volumeNumber 4
    51 rdf:type schema:PublicationVolume
    52 Nc200db170ed149c3a2468a066ee9d13a schema:name Springer Nature - SN SciGraph project
    53 rdf:type schema:Organization
    54 Nd9cbf5224a0f4ccc85061fffc135092c schema:name readcube_id
    55 schema:value ad26bc473eb54309c98459f0bd6c324328b6a99687624d634b780e9026dab4bf
    56 rdf:type schema:PropertyValue
    57 sg:journal.1136382 schema:issn 1382-4090
    58 1572-9303
    59 schema:name The Ramanujan Journal
    60 rdf:type schema:Periodical
    61 sg:person.07704611215.01 schema:affiliation https://www.grid.ac/institutes/grid.16750.35
    62 schema:familyName Pribitkin
    63 schema:givenName Wladimir De Azevedo
    64 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07704611215.01
    65 rdf:type schema:Person
    66 sg:pub.10.1007/bf01187948 schema:sameAs https://app.dimensions.ai/details/publication/pub.1012764582
    67 https://doi.org/10.1007/bf01187948
    68 rdf:type schema:CreativeWork
    69 sg:pub.10.1007/bf01388796 schema:sameAs https://app.dimensions.ai/details/publication/pub.1023784435
    70 https://doi.org/10.1007/bf01388796
    71 rdf:type schema:CreativeWork
    72 sg:pub.10.1007/bf01390728 schema:sameAs https://app.dimensions.ai/details/publication/pub.1044380812
    73 https://doi.org/10.1007/bf01390728
    74 rdf:type schema:CreativeWork
    75 https://doi.org/10.1070/sm1981v039n03abeh001518 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058199930
    76 rdf:type schema:CreativeWork
    77 https://doi.org/10.1073/pnas.23.2.78 schema:sameAs https://app.dimensions.ai/details/publication/pub.1038275601
    78 rdf:type schema:CreativeWork
    79 https://doi.org/10.1090/pspum/049.2/1013169 schema:sameAs https://app.dimensions.ai/details/publication/pub.1089196869
    80 rdf:type schema:CreativeWork
    81 https://doi.org/10.1090/s0002-9947-1974-0344196-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1028240869
    82 rdf:type schema:CreativeWork
    83 https://doi.org/10.1112/plms/s2-17.1.75 schema:sameAs https://app.dimensions.ai/details/publication/pub.1009143639
    84 rdf:type schema:CreativeWork
    85 https://doi.org/10.1112/plms/s2-43.4.241 schema:sameAs https://app.dimensions.ai/details/publication/pub.1009388005
    86 rdf:type schema:CreativeWork
    87 https://doi.org/10.1515/crll.1877.83.265 schema:sameAs https://app.dimensions.ai/details/publication/pub.1049127938
    88 rdf:type schema:CreativeWork
    89 https://doi.org/10.1515/crll.1967.227.86 schema:sameAs https://app.dimensions.ai/details/publication/pub.1025554343
    90 rdf:type schema:CreativeWork
    91 https://doi.org/10.2307/1968973 schema:sameAs https://app.dimensions.ai/details/publication/pub.1069674378
    92 rdf:type schema:CreativeWork
    93 https://doi.org/10.2307/1971381 schema:sameAs https://app.dimensions.ai/details/publication/pub.1069676654
    94 rdf:type schema:CreativeWork
    95 https://doi.org/10.4064/aa-91-4-291-309 schema:sameAs https://app.dimensions.ai/details/publication/pub.1092041515
    96 rdf:type schema:CreativeWork
    97 https://doi.org/10.4064/aa-93-4-343-358 schema:sameAs https://app.dimensions.ai/details/publication/pub.1101092722
    98 rdf:type schema:CreativeWork
    99 https://www.grid.ac/institutes/grid.16750.35 schema:alternateName Princeton University
    100 schema:name Department of Mathematics, Princeton University, 607 Fine Hall, Washington Road, 08544-1000, Princeton, New Jersey
    101 rdf:type schema:Organization
     




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


    ...