A general simple relative trace formula

In this paper we prove a relative trace formula for all pairs of connected algebraic groups H ≤ G × G, with G a reductive group and H the direct product of a reductive group and a unipotent group, given that the test function satisfies simplifying hypotheses. As an application, we prove a relative analogue of the Weyl law, giving an asymptotic formula for the number of eigenfunctions of the Laplacian on a locally symmetric space associated to G weighted by their L²-restriction norm over a locally symmetric subspace associated to H0 ≤ G.

Duke Scholars

Author Jayce Robert Getz Mathematics

Author Heekyoung Hahn Mathematics