The Relative Trace Formula and Central L-values

Andrew Knightly, Principal Investigator; University of Maine, Orono

Graduate Student

John Jackson
Carl Ragsdale

Abstract

The goal of this project is to develop new explicit relative trace formulas on GL(2) and higher rank groups, and explore applications to the analytic theory of L-functions.

There were five major activities carried out during the period supported by this grant, to be described in greater detail in the "Significant results" section below. These were:

1. A generalized Kuznetsov formula with application to equidistribution of Maass form Hecke eigenvalues.
2. A new formula for averages of twisted L-functions.
3. A treatment of simple supercuspidal representations of GL(n), with explicit computation of matrix coefficients.
4. An average value formula for twisted L-functions of newforms of cubic level.
5. A calculation of matrix coefficients of depth-zero supercuspidal representations of GL(2).