Ramanujan series upside-down

Abstract

We prove that there is a correspondence between Ramanujan-type formulas for 1/π, 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.

28 pages

References in corpus (1)

• Dirichlet L-series with real and complex characters and their application to solving double sums

Cited by in corpus (6)

• New series for some special values of $L$-functions
• A Hypergeometric Version of the Modularity of Rigid Calabi-Yau Manifolds
• Kind of proofs of Ramanujan-like series
• Bilateral sums related to Ramanujan-like series
• Rational Hypergeometric Ramanujan Identities for $1/{\pi }^c$: Survey and Generalizations
• New type series for powers of $\pi$