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Some Eisenstein Series Identities

✍ Scribed by Zhi-Guo Liu

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 151 KB
Volume: 85
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.2000.2543

No coin nor oath required. For personal study only.

✦ Synopsis

dedicated to bruce c. berndt on the occasion of his 60th birthday

In this paper we use the theory of elliptic functions to provide different proofs of some Eisenstein series identities of Ramanujan from those given in a recent paper by B. C. Berndt, S. Bhargava, and F. G. Garvan (1995, Trans. Amer. Math. Soc. 347, 4136 4244). From one of these identities we derive the inversion formula for the Borweins cubic theta functions via Venkatachanliengar's method. We also derive some striking Eisenstein series identities associated with the Borweins' cubic theta functions.

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