Quantum Unique Ergodicity for Eisenstein Series on the Hilbert Modular Group over a Totally Real Field

Date
Authors
Truelsen, Jimi Lee
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
Description
W. Luo and P. Sarnak have proved the quantum unique ergodicity property for Eisenstein series on $\rm{PSL}(2,\mathbb{Z}) \backslash H$. We extend their result to Eisenstein series on $\rm{PSL}(2,O) \backslash H^n$, where $O$ is the ring of integers in a totally real field of degree $n$ over $Q$ with narrow class number one, using the Eisenstein series considered by I. Efrat. We also give an expository treatment of the theory of Hecke operators on non-holomorphic Hilbert modular forms.
Comment: 28 pages
Keywords
Mathematics - Number Theory, 11M06, 81Q50, 11F41
Citation
Collections