On Ramanujan's modular identities
type: Item
instance of: scholarly article
title: On Ramanujan's modular identities
zbMATH Open document ID: 0655.10011
DOI: 10.1007/BF02837829
author: S. H. Smith
published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences
publication date: 1987-01-01T00:00:00Z
review text: Ramanujan's partition congruences \(p(5n+4)\equiv 0 (mod 5)\) and \(p(7n+5)\equiv 0 (mod 7)\) can be derived by equating coefficients in various modular identities. In an earlier paper [Q. J. Math., Oxf. II. Ser. 37, 221-229 (1986; Zbl 0585.10033)] the author derived these identities with the use of modular forms. This note extends the method to the more difficult case of modulus 11 and also relates this work to that of \textit{N. J. Fine} [Tôhoku Math. J., II. Ser. 8, 149-164 (1956; Zbl 0073.029)].
Mathematics Subject Classification ID: 11P81
Mathematics Subject Classification ID: 11F11
Mathematics Subject Classification ID: 11F99
zbMATH DE Number: 4068971
zbMATH Keywords: Ramanujan's partition congruences
zbMATH Keywords: modular identities
zbMATH Keywords: modular forms
MaRDI profile type: Publication
cites work: A NOTE ON TWO OF RAMANUJAN'S FORMULAE
cites work: A FURTHER NOTE ON TWO OF RAMANUJAN'S FORMULAE
cites work: On a system of modular functions connected with the Ramanujan identities
cites work: Q3267357
cites work: ON CERTAIN IDENTITIES DUE TO RAMANUJAN
cites work: Q4402037
cites work: Q4723820
full work available at URL: https://doi.org/10.1007/bf02837829
OpenAlex ID: W1983921285
description: scientific article; zbMATH DE number 4068971