An analogue of the Mellin transform for weakly holomorphic cusp forms and a converse theorem

IF 0.8 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2024-09-27 DOI:10.1112/blms.13163

Ö. Imamoḡlu, Y. Martin, Á. Tóth

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引用次数: 0

Abstract

We define an analogue of the classical Mellin transform for vector-valued weakly holomorphic cusp forms for $S L (2, Z)$ and prove a converse theorem for such forms in terms of the new transform. As applications we get converse theorems for scalar valued weakly holomorphic forms for $S L (2, Z)$ as well as $Γ_{0} (p)$ for primes $p$ .

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弱全纯尖形的Mellin变换的一个类似性质及一个逆定理

我们定义了SL(2， Z)$ SL(2,\mathbb {Z})$的向量值弱全纯尖形的经典Mellin变换的一个类似物，并利用这个新变换证明了这种形式的一个逆定理。作为应用，得到了S L(2)的标量值弱全纯形式的逆定理。Z)$ SL(2,\mathbb {Z})$以及Γ 0(p)$ \Gamma _0(p)$用于质数p$ p$。

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