Ramanujan's elementary method in partition congruences

Bruce C Berndt, Chadwick Gugg, Sun Kim

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

Page 182 in Ramanujan's lost notebook corresponds to page 5 of an otherwise lost manuscript of Ramanujan closely related to his paper providing elementary proofs of his partition congruences p(5n + 4) ≡ 0 (mod 5) and p(7n+5) ≡ 0 (mod 7). The claims on page 182 are proved and discussed, and further results depending on Ramanujan's ideas are established.

Original languageEnglish (US)
Title of host publicationPARTITIONS, Q-SERIES, AND MODULAR FORMS
EditorsKRISHNASWAMI ALLADI, FRANK GARVAN
Pages13-21
Number of pages9
DOIs
StatePublished - Apr 12 2012

Publication series

NameDevelopments in Mathematics
Volume23
ISSN (Print)1389-2177

Keywords

  • Congruences
  • Jacobi's identity
  • Partitions
  • Pentagonal number theorem
  • Winquist's identity

ASJC Scopus subject areas

  • Mathematics(all)

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