The sixth, eighth, ninth, and tenth powers

of Ramanujan's theta function

Author:
Scott Ahlgren

Journal:
Proc. Amer. Math. Soc. **128** (2000), 1333-1338

MSC (1991):
Primary 11B65, 33D10

Published electronically:
October 6, 1999

MathSciNet review:
1646322

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Abstract | References | Similar Articles | Additional Information

Abstract: In his Lost Notebook, Ramanujan claimed that the ``circular'' summation of the -th powers of the symmetric theta function satisfies a factorization of the form . Moreover, Ramanujan recorded identities expressing , , , , and in terms of his theta functions , , and . Ramanujan's claims were proved by Rangachari, and later (via elementary methods) by Son. In this paper we obtain similar identities for , , , and .

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Additional Information

**Scott Ahlgren**

Affiliation:
Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802-6401

Address at time of publication:
Department of Mathematics, Colgate University, Hamilton, New York 13346

Email:
ahlgren@math.psu.edu

DOI:
https://doi.org/10.1090/S0002-9939-99-05181-3

Keywords:
Ramanujan,
theta functions

Received by editor(s):
July 10, 1998

Published electronically:
October 6, 1999

Communicated by:
David E. Rohrlich

Article copyright:
© Copyright 2000
American Mathematical Society