Apery limits and special values of L-functions

Abstract

We describe a general method to determine the Apery limits of a differential equation that has a modular-function origin. As a by-product of our analysis, we discover a family of identities involving the special values of L-functions associated with modular forms. The proof of these identities is independent of differential equations and Apery limits. (C) 2008 Elsevier Inc. All rights reserved.