Massive deformations of Maass forms and Jacobi forms

TL;DR

This paper introduces one-parameter massive deformations of Maass and Jacobi forms, inspired by string theory, including examples like massive Green's functions and modular graph functions.

Contribution

It defines and explores massive deformations of classical automorphic forms, connecting them to concepts in string theory and providing explicit examples.

Findings

Massive Green's functions expressed via Kronecker-Eisenstein series

Introduction of massive modular graph functions

New framework linking automorphic forms to string theory phenomena

Abstract

We define one-parameter "massive" deformations of Maass forms and Jacobi forms. This is inspired by descriptions of plane gravitational waves in string theory. Examples include massive Green's functions (that we write in terms of Kronecker-Eisenstein series) and massive modular graph functions.