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

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

2007-06-28

arxiv.org/abs/0706.4239v3

Mathematics

Number Theory

28 pages

Scientific paper

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.

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