Quantum variance on quaternion algebras, I
Number Theory
2016-11-15 v2 Dynamical Systems
Abstract
We determine the quantum variance of a sequence of families of automorphic forms on a compact quotient arising from a non-split quaternion algebra. Our results compare to those obtained by Luo--Sarnak, Zhao, and Sarnak--Zhao on the modular curve, whose method required a cusp. Our method uses the theta correspondence to reduce the problem to the estimation of metaplectic Rankin--Selberg convolutions. We apply it here to the first non-split case.
Cite
@article{arxiv.1601.02526,
title = {Quantum variance on quaternion algebras, I},
author = {Paul D. Nelson},
journal= {arXiv preprint arXiv:1601.02526},
year = {2016}
}
Comments
39 pages; minor edits, corrections, and rearrangements of the text; second proof of Prop 3 added