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

Abstract

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

The second mollified moments are not properly computed. Also, the inverse convolution of λ_f(n) is incorrectly defined. Please withdraw all versions