Simple zeros of automorphic $L$-functions

TL;DR

This paper proves that the complete L-function of any cuspidal automorphic representation of GL(2) over Q has infinitely many simple zeros, advancing understanding of zero distributions in automorphic L-functions.

Contribution

It establishes the infinitude of simple zeros for the complete L-function associated with any cuspidal automorphic representation of GL(2) over Q, a new result in automorphic L-function theory.

Findings

Complete L-functions of cuspidal automorphic representations of GL(2) have infinitely many simple zeros.

The result applies to all such automorphic representations over Q.

It provides new insights into the zero distribution of automorphic L-functions.

Abstract

We prove that the complete $L$-function associated to any cuspidal automorphic representation of $GL_2(\mathbb{A}_{\mathbb Q})$ has infinitely many simple zeros.