Vol. 277, No. 1, 2015

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ISSN: 0030-8730
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 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.

Keywords
relative trace formula, Weyl law
Mathematical Subject Classification 2010
Primary: 11F70
Secondary: 35P20
Milestones
Received: 30 October 2014
Revised: 17 February 2015
Accepted: 25 February 2015
Published: 6 August 2015
Authors
Jayce R. Getz
Department of Mathematics
Duke University
Durham, NC 27708-0320
United States
Heekyoung Hahn
Department of Mathematics
Duke University
Durham, NC 27708-0320
United States