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.

arXiv comment16+3 pages, published version

References in corpus (6)

• Elliptic multiple zeta values and one-loop superstring amplitudes
• On the modular structure of the genus-one Type II superstring low energy expansion
• Eisenstein series and automorphic representations
• Modular Invariance of Strings on PP-Waves with RR-flux
• Simpler Superstring Scattering
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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