Massive deformations of Maass forms and Jacobi forms

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.

16+3 pages, published version

References in corpus (2)

• Simpler Superstring Scattering
• A solution manual for Polchinski's "String Theory"

Cited by in corpus (6)

• The SAGEX Review on Scattering Amplitudes, Chapter 10: Selected topics on modular covariance of type IIB string amplitudes and their $\mathcal{N}=4$ supersymmetric Yang-Mills duals
• Poincaré series for modular graph forms at depth two. II. Iterated integrals of cusp forms
• Poincaré series for modular graph forms at depth two. I. Seeds and Laplace systems
• $T\overline{T}$-deformed modular forms
• Massive Theta Lifts
• Fourier expansions of vector-valued automorphic functions with non-unitary twists