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arXiv · 0706.4239

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

Jimi Lee Truelsen
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Abstract

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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Jimi Lee Truelsen. 2008-11-18. Quantum Unique Ergodicity for Eisenstein Series on the Hilbert Modular Group over a Totally Real Field. https://arxiv.org/abs/0706.4239

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