The Relative Trace Formula and Central L-values
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:
- A generalized Kuznetsov formula with application to equidistribution of Maass form Hecke eigenvalues.
- A new formula for averages of twisted L-functions.
- A treatment of simple supercuspidal representations of GL(n), with explicit computation of matrix coefficients.
- An average value formula for twisted L-functions of newforms of cubic level.
- A calculation of matrix coefficients of depth-zero supercuspidal representations of GL(2).