Arithmetic properties of ℓ-regular partitions

For a given prime p, by studying p-dissection identities for Ramanujanʼs theta functions ψ(q) and f(−q), we derive infinite families of congruences modulo 2 for some ℓ-regular partition functions, where ℓ=2,4,5,8,13,16.

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Bibliographic Details
Published inAdvances in applied mathematics Vol. 51; no. 4; pp. 507 - 523
Main Authors Cui, Su-Ping, Gu, Nancy S.S.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.09.2013
Subjects
Congruence
Ramanujanʼs theta function
ℓ-regular partition
Ramanujanʼs theta function
11P83
ℓ-regular partition
Congruence
05A17
Online AccessGet full text
ISSN0196-8858
1090-2074
DOI10.1016/j.aam.2013.06.002

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Summary:For a given prime p, by studying p-dissection identities for Ramanujanʼs theta functions ψ(q) and f(−q), we derive infinite families of congruences modulo 2 for some ℓ-regular partition functions, where ℓ=2,4,5,8,13,16.
ISSN:0196-8858
1090-2074
DOI:10.1016/j.aam.2013.06.002