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A three-term theta function identity and its applications. (English) Zbl 1138.11014

The author of the paper under review uses the complex variable theory of elliptic functions to establish interesting theta function identities. He uses these identities in order to derive a new proof of the addition theorem for the Weierstrass elliptic function \(\wp\), and some identities for Eisenstein series which have been found in Ramanujan’s lost notebook. These identities have been proven before by B. C. Berndt and A. J. Yee but here the approach is different.

MSC:

11F27 Theta series; Weil representation; theta correspondences
33E05 Elliptic functions and integrals
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