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

Abstract

W. Luo and P. Sarnak have proved the quantum unique ergodicity property for Eisenstein series on $\mathrm{PSL}(2,\mathbb{Z})\backslash H$. We extend their result to Eisenstein series on $\mathrm{PSL}(2,\mathrm{O})\backslash {\mathrm{H}}^{\mathrm{n}}$, 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.

28 pages

References in corpus (1)

• Mass equidistribution for Hecke eigenforms