L-Series for Vector-Valued Weakly Holomorphic Modular Forms and Converse Theorems
Abstract
We introduce the L-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.
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