Beyond the Selberg Class: $0\le d_F\le 2$

Abstract: I will define a class of Dirichlet series $\mathfrak{A}^{#}$ which strictly contains the extended Selberg class as well as several $L$-functions (including the tensor product, symmetric square and exterior square $L$-functions of automorphic representations of $GL_n$. I will describe a number of classification results which generalise the work of Kaczorowski and Perelli and provide simpler proofs in many cases. Time permitting, I will discuss some applications concerning the zero sets of $L$ functions. Some of the results have been obtained in collaboration with R. Balasubramanian.

number theory

Audience: researchers in the topic

Number theory during lockdown

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