Weyl’s law for SL(3, ℤ)∖SL(3, ℝ)∕SO(3, ℝ)

Eric George Stade and Dorothy Irene Wallace

Vol. 173 (1996), No. 1, 241–261

DOI: 10.2140/pjm.1996.173.241

Abstract

In this paper we derive a Weyl’s law, or asymptotic description of the distribution of eigenvalues of the Laplacian, on SL(3, ℤ)∖SL(3, ℝ)∕SO(3, ℝ). Our main tool in this derivation is the Selberg trace formula for the space. Our Weyl’s law, which refines the present theory for the space in question, is also seen to coincide with known results in the case where SL(3, ℤ) is replaced by a cocompact discrete subgroup.

Mathematical Subject Classification 2000

Primary: 11F72

Milestones

Received: 17 August 1993

Revised: 31 March 1994

Published: 1 March 1996