Some Eisenstein series identities related to modular equations of the seventh order
- 1 March 2003
- journal article
- Published by Mathematical Sciences Publishers in Pacific Journal of Mathematics
- Vol. 209 (1), 103-130
- https://doi.org/10.2140/pjm.2003.209.103
Abstract
In this paper we will use one well-known modular equation of seventh order, one theta function identity of S. McCullough and L.-C. Shen, 1994, and the complex variable theory of el- liptic functions to prove some new septic identities for theta functions. Then we use these identities to provide new proofs of some Eisenstein series identities in Ramanujan's notebooks or "lost" notebook. We also derive a new identity for Eisen- stein series and some curious trigonometric identities.Keywords
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