School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Differential equations for septic theta functions

Document Type

Article

Publication Date

7-29-2014

Abstract

We demonstrate that quotients of septic theta functions appearing in Ramanujan’s Notebooks and in Klein’s work satisfy a new coupled system of nonlinear differential equations with symmetric form. This differential system bears a close resemblance to an analogous system for quintic theta functions. The proof extends an elementary technique used by Ramanujan to prove the classical differential system for normalized Eisenstein series on the full modular group. In the course of our work, we show that Klein’s quartic relation induces symmetric representations for low-weight Eisenstein series in terms of weight one modular forms of level seven.

Comments

Copyright © 2014, Springer Science Business Media New York

https://rdcu.be/c56l2

Publication Title

Ramanujan J

DOI

10.1007/s11139-014-9588-1

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