#### Vol. 277, No. 1, 2015

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A general simple relative trace formula

### Jayce R. Getz and Heekyoung Hahn

Vol. 277 (2015), No. 1, 99–118
##### Abstract

In this paper we prove a relative trace formula for all pairs of connected algebraic groups $H\le G×G$, 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 ${L}^{\mathfrak{2}}$-restriction norm over a locally symmetric subspace associated to ${H}_{\mathfrak{0}}\le G$.

##### Keywords
relative trace formula, Weyl law
Primary: 11F70
Secondary: 35P20