Selberg's Central Limit Theorem for automorphic $L$-functions in the $t$-aspect

TL;DR

This paper proves Selberg's Central Limit Theorem for degree 2 automorphic L-functions in the t-aspect and establishes their independence for primitive holomorphic cusp forms, advancing understanding of their probabilistic behavior.

Contribution

It introduces a proof of Selberg's CLT for degree 2 automorphic L-functions using recent methods and demonstrates their independence, which is a novel result.

Findings

Proved Selberg's CLT for automorphic L-functions of degree 2

Established independence of automorphic L-functions for primitive cusp forms

Applied Radziwi
4ll and Soundararajan's method to this context

Abstract

We present a proof of Selberg's Central Limit Theorem for automorphic $L$-functions of degree 2 using Radziwi\l\l\space and Soundararajan's method. Additionally, we prove the independence of the automorphic $L$-functions associated with the sequence of primitive holomorphic cusp forms.