Hecke-Maass cusp forms on PGL_n of large levels with non-vanishing L-values

TL;DR

This paper develops a new trace formula connecting L-values and Whittaker periods of automorphic forms on PGL_n, demonstrating infinitely many forms with non-vanishing L-values at multiple points.

Contribution

It introduces a novel Kuznetsov-type trace formula involving central L-values and Whittaker periods for PGL_n, enabling new non-vanishing results.

Findings

Proves simultaneous non-vanishing of L-values at multiple points.

Establishes a trace formula linking L-values and automorphic representations.

Shows existence of infinitely many forms with desired non-vanishing properties.

Abstract

We introduce a new trace formula of Kuznetsov type involving the central standard L-values and the Whittaker periods of cuspidal automorphic representations of PGL_n(Q) which are spherical at the archimedean place. As an application, we show a simultaneous non-vanishing of standard L-values at n-1 points on the critical strip for infinitely many Hecke-Maass cuspidal newforms.