Transformation formulas for the higher power of odd zeta values and generalized Eisenstein series

TL;DR

This paper derives a transformation formula for higher powers of odd zeta values, extending Ramanujan's work, and explores applications to Eisenstein series and Dedekind eta functions.

Contribution

It introduces a generalized transformation formula for higher odd zeta powers, expanding the scope of Ramanujan's classical results.

Findings

Generalized transformation formula for higher odd zeta powers

Extensions to Eisenstein series and Dedekind eta function transformations

New applications demonstrating the formula's broad relevance

Abstract

In this article, we obtain a transformation formula for the higher power of odd zeta values, which generalizes Ramanujan's formula for odd zeta values. We have also investigated many important applications, which in turn provide generalizations of the transformation formula of the Eisenstein series, Dedekind eta function etc.