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Quantum unique ergodicity of Eisenstein series on the Hilbert modular group over a totally real field
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Jimi L. Truelsen
Published/Copyright:
April 14, 2010
Abstract
W. Luo and P. Sarnak have proved the quantum unique ergodicity property for Eisenstein series on PSL(2, ℤ)\ℍ. Their result is quantitative in the sense that they find the precise asymptotics of the measure considered. We extend their result to Eisenstein series on 
, 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.
Received: 2008-10-01
Revised: 2009-11-02
Published Online: 2010-04-14
Published in Print: 2011-September
© de Gruyter 2011
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Articles in the same Issue
- Quantum unique ergodicity of Eisenstein series on the Hilbert modular group over a totally real field
- On the self-intersection cycle of surfaces and some classical formulas for their secant varieties
- Wolff potentials and the 3-d wave operator
- Statistics for low-lying zeros of symmetric power L-functions in the level aspect
- Simple Harish-Chandra modules, intermediate series modules, and Verma modules over the loop-Virasoro algebra
- On the classification of fake lens spaces
- Cohomology and removable subsets
