A new class of theta-function identities originating in Ramanujan's notebooks
type: Item
instance of: scholarly article
title: A new class of theta-function identities originating in Ramanujan's notebooks
zbMATH Open document ID: 0812.11028
author: Bruce C. Berndt
author: Liang-Cheng Zhang
published in: Journal of Number Theory
publication date: 1994-09-28T00:00:00Z
review text: The authors use the theory of modular forms to prove a common generalization of two distinctive theta-function identities stated by Ramanujan. The simpler of Ramanujan's identities is \[ {\textstyle { {{u^ 2} \over v}- {{v^ 2} \over w} + {{w^ 2} \over u}}} =0, \] where \(u= \sum (-1)^ n q^{(7/2) (n-1/ 14)^ 2}\), \(v= \sum (-1)^ n q^{(7/2) (n-3/ 14)^ 2}\), \(w= \sum (-1)^ n q^{(7/2) (n-5/ 14)^ 2}\).
Mathematics Subject Classification ID: 11F11
Mathematics Subject Classification ID: 11P82
zbMATH DE Number: 645295
zbMATH Keywords: modular forms
zbMATH Keywords: theta-function identities
zbMATH Keywords: Ramanujan's identities
reviewed by: David M. Bressoud
MaRDI profile type: Publication
full work available at URL: jnth.1994.1064
OpenAlex ID: W2053691435
DOI: 10.1006/JNTH.1994.1064
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description: scientific article; zbMATH DE number 645295