Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

A theta function identity and its implications
HTML articles powered by AMS MathViewer

by Zhi-Guo Liu PDF
Trans. Amer. Math. Soc. 357 (2005), 825-835 Request permission

Abstract:

In this paper we prove a general theta function identity with four parameters by employing the complex variable theory of elliptic functions. This identity plays a central role for the cubic theta function identities. We use this identity to re-derive some important identities of Hirschhorn, Garvan and Borwein about cubic theta functions. We also prove some other cubic theta function identities. A new representation for $\prod _{n=1}^\infty (1-q^n)^{10}$ is given. The proofs are self-contained and elementary.
References
Similar Articles
Additional Information
  • Zhi-Guo Liu
  • Affiliation: Department of Mathematics, East China Normal University, Shanghai 200062, People’s Republic of China
  • MR Author ID: 364722
  • Email: zgliu@math.ecnu.edu.cn, liuzg18@hotmail.com
  • Received by editor(s): September 18, 2003
  • Received by editor(s) in revised form: October 24, 2003
  • Published electronically: September 2, 2004
  • Additional Notes: The author was supported in part by Shanghai Priority Academic Discipline and the National Science Foundation of China
  • © Copyright 2004 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 357 (2005), 825-835
  • MSC (2000): Primary 11F11, 11F12, 11F27, 33E05
  • DOI: https://doi.org/10.1090/S0002-9947-04-03572-X
  • MathSciNet review: 2095632