Simple functional equations for generalized Selberg zeta functions with Tate motives

TL;DR

This paper demonstrates that for certain compact symmetric spaces, there are infinitely many automorphic Tate motives for which the associated generalized Selberg zeta functions satisfy a simple functional equation without gamma factors.

Contribution

It establishes the existence of infinitely many automorphic Tate motives leading to simplified functional equations for generalized Selberg zeta functions.

Findings

Existence of infinitely many automorphic Tate motives for rank 1 spaces.

Generalized Selberg zeta functions satisfy simple functional equations.

No gamma factors are involved in these functional equations.

Abstract

We prove that for a compact locally symmetric Riemannian space $M$ of rank 1 there exist infinitely many automorphic Tate motives $f$ such that the generalized Selberg zeta function $Z_{M(f)}(s)$ satisfies a simple functional equation in the sense that it has no gamma factors.