Ramanujan series upside-down

TL;DR

This paper establishes a connection between Ramanujan-type formulas for 1/π, Dirichlet L-values, and Epstein zeta functions, providing new methods for evaluating these special functions using hypergeometric series.

Contribution

It introduces a novel method linking Ramanujan formulas, Dirichlet L-values, and Epstein zeta functions, enabling new evaluations of these functions.

Findings

Established correspondence between Ramanujan formulas and Dirichlet L-values

Resolved certain Epstein zeta function values using hypergeometric functions

Extended previous work by Glasser and Zucker on Epstein zeta functions

Abstract

We prove that there is a correspondence between Ramanujan-type formulas for 1/\pi, and formulas for Dirichlet L-values. The same method also allows us to resolve certain values of the Epstein zeta function in terms of rapidly converging hypergeometric functions. The Epstein zeta functions were previously studied by Glasser and Zucker.