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

2007/06/28 by Jimi Lee Truelsen, Truelsen, Jimi Lee
Mathematics · #11F41 #11M06 #81Q50 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.0706.4239

openalex publication_date 2007/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

W. Luo and P. Sarnak have proved the quantum unique ergodicity property for Eisenstein series on \rmPSL(2,ℤ) \backslash H. We extend their result to Eisenstein series on \rmPSL(2,O) \backslash Hⁿ, 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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