Communications in Number Theory and Physics

Volume 15 (2021)

Number 3

Massive deformations of Maass forms and Jacobi forms

Pages: 575 – 603



Marcus Berg (Department of Physics, Karlstad University, Karlstad, Sweden)

Kathrin Bringmann (Department of Mathematics and Computer Science, University of Cologne, Germany)

Terry Gannon (Department of Mathematics, University of Alberta, Edmonton, ALB, Canada)


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.

2010 Mathematics Subject Classification

Primary 11F50. Secondary 11F30, 11F37.

The research of the second author is supported by the Alfried Krupp Prize for Young University Teachers of the Krupp foundation. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 101001179).

The research of the third author is supported in part by an NSERC Discovery Grant.

Received 24 October 2019

Accepted 28 March 2021

Published 15 July 2021