Apery limits and special values of L-functions

TL;DR

This paper introduces a method to find Apery limits linked to modular functions and uncovers new identities involving special L-function values, independent of differential equations.

Contribution

It presents a novel approach to determine Apery limits with modular origins and discovers new identities for L-functions associated with modular forms.

Findings

A general method for Apery limits with modular origins

New identities involving special values of L-functions

Independent proof of these identities from differential equations

Abstract

We describe a general method to determine the Apery limits of a differential equation that have 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.