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Mass equidistribution of Hecke eigenforms on the Hilbert modular varieties
Liu, Sheng-Chi

2009, Doctor of Philosophy, Ohio State University, Mathematics.

In this thesis we study the analogue of Arithmetic Quantum Unique
Ergodicity conjecture on the Hilbert modular variety. Let F
be a totally real number field with ring of integers 𝒪, and
let Γ = SL(2, 𝒪) be the Hilbert modular group. Given the
orthonormal basis of Hecke eigenforms in S2k(Γ),
the space of cusp forms of weight (2k, 2k,⋯, 2k),
one can associate a probability measure k
on the Hilbert modular variety Γ\ℍn. We
prove that k tends to the invariant measure on
Γ\ℍn weakly as k → ∞. This
shows that the analogue of Arithmetic Quantum Unique Ergodicity conjecture
is true on the average on Hilbert modular variety. Our result generalizes
Luo’s result [Lu] for the case F = ℚ.



Our approach is using Selberg trace formula, Bergman kernel, and
Shimizu’s dimension formula.


Wenzhi Luo (Advisor)
James Cogdell (Committee Member)
Robert Stanton (Committee Member)
42 p.

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Liu, S. (2009). Mass equidistribution of Hecke eigenforms on the Hilbert modular varieties. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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Liu, Sheng-Chi. "Mass equidistribution of Hecke eigenforms on the Hilbert modular varieties." Electronic Thesis or Dissertation. Ohio State University, 2009. OhioLINK Electronic Theses and Dissertations Center. 25 Sep 2017.

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Liu, Sheng-Chi "Mass equidistribution of Hecke eigenforms on the Hilbert modular varieties." Electronic Thesis or Dissertation. Ohio State University, 2009. https://etd.ohiolink.edu/

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