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L-Series for Vector-Valued Weakly Holomorphic Modular Forms and Converse Theorems

arXiv:2409.04258 · doi:10.4153/S0008414X24001160

Abstract

We introduce the -series of weakly holomorphic modular forms using Laplace transforms and give their functional equations. We then determine converse theorems for vector-valued harmonic weak Maass forms, Jacobi forms, and elliptic modular forms of half-integer weight in Kohnen plus space.

L-Series for Vector-Valued Weakly Holomorphic Modular Forms and Converse Theorems · wovepaper