On the zeros of Weng zeta functions for Chevalley groups

TL;DR

This paper proves that, under certain geometric conditions, all but finitely many zeros of Weng's zeta functions for Chevalley groups are simple and located on the critical line, advancing understanding of their zero distribution.

Contribution

It establishes the simplicity and critical line location of almost all zeros of Weng's zeta functions for Chevalley groups under geometric hypotheses.

Findings

Almost all zeros are simple and on the critical line.

Finitely many zeros may lie off the critical line.

Provides conditions under which zero distribution properties hold.

Abstract

We prove that all but finitely many zeros of Weng's zeta function for a Chevalley group defined over $\Q$ are simple and on the critical line under some reasonable geometric hypothesis.