Ramanujan's elementary method in partition congruences

Bruce C. Berndt; Chadwick Gugg; Sun Kim

doi:10.1007/978-1-4614-0028-8_2

Ramanujan's elementary method in partition congruences

Bruce C. Berndt
, Chadwick Gugg
, Sun Kim

Department of Mathematics

University of Illinois at Urbana-Champaign
Georgia Southwestern State University
Pennsylvania State University

Research output: Contribution to conference › Chapter › peer-review

3 Scopus citations

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 language	English
Title of host publication	PARTITIONS, Q-SERIES, AND MODULAR FORMS
Editors	KRISHNASWAMI ALLADI, FRANK GARVAN
Pages	13-21
Number of pages	9
DOIs	https://doi.org/10.1007/978-1-4614-0028-8_2
State	Published - 2012

Publication series

Name	Developments in Mathematics
Volume	23
ISSN (Print)	1389-2177

Keywords

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

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10.1007/978-1-4614-0028-8_2

Cite this

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KW - Congruences

KW - Jacobi's identity

KW - Partitions

KW - Pentagonal number theorem

KW - Winquist's identity

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Ramanujan's elementary method in partition congruences

Abstract

Publication series

Keywords

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