On a conjecture of Koike on identities between Thompson series and Rogers-Ramanujan functions

Authors:
Kathrin Bringmann and Holly Swisher

Journal:
Proc. Amer. Math. Soc. **135** (2007), 2317-2326

MSC (2000):
Primary 11F22, 33D15, 11F03

DOI:
https://doi.org/10.1090/S0002-9939-07-08735-7

Published electronically:
March 21, 2007

Erratum:
Proc. Amer. Math. Soc. 136 (2008), 1501-1501.

MathSciNet review:
2302552

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: One of the many amazing things Ramanujan did in his lifetime was to list identities involving what are now called the Rogers-Ramanujan functions and on one side, and products of functions of the form on the other side. The identities are rather complicated and seem too difficult to guess. Recently however, Koike devised a strategy for finding (but not proving) these types of identities by connecting them to Thompson series. He was able to conjecture many new Rogers-Ramanujan type identities between and , and Thompson series. Here we prove these identities.

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Additional Information

**Kathrin Bringmann**

Affiliation:
Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706

Email:
bringman@math.wisc.edu

**Holly Swisher**

Affiliation:
Department of Mathematics, The Ohio State University, Columbus, Ohio 43210

Email:
swisher@math.ohio-state.edu

DOI:
https://doi.org/10.1090/S0002-9939-07-08735-7

Received by editor(s):
January 31, 2006

Received by editor(s) in revised form:
March 27, 2006

Published electronically:
March 21, 2007

Communicated by:
Ken Ono

Article copyright:
© Copyright 2007
American Mathematical Society