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

Subong Lim, Wissam Raji
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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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矢量值弱全态模态的 L 序列和逆定理
我们利用拉普变换介绍弱全态模形式的 $L$ 系列,并给出它们的函数方程。然后,我们确定了科嫩加空间中矢量值谐弱马斯形式、雅可比形式和半整数权的椭圆模形式的会话定理。
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