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Mass equidistribution for automorphic forms of cohomological type on $ GL_2$


Author: Simon Marshall
Journal: J. Amer. Math. Soc. 24 (2011), 1051-1103
MSC (2010): Primary 11F41, 11F11; Secondary 11F75
DOI: https://doi.org/10.1090/S0894-0347-2011-00700-5
Published electronically: April 6, 2011
Erratum: J. Amer. Math. Soc. 25 (2012), 615-616
MathSciNet review: 2813338
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Abstract | References | Similar Articles | Additional Information

Abstract: We extend Holowinsky and Soundararajan's proof of quantum unique ergodicity for holomorphic Hecke modular forms on $ SL(2,\mathbb{Z})$, by establishing it for automorphic forms of cohomological type on $ GL_2$ over an arbitrary number field which satisfy the Ramanujan bounds. In particular, we have unconditional theorems over totally real and imaginary quadratic fields. In the totally real case we show that our result implies the equidistribution of the zero divisors of holomorphic Hecke modular forms, generalising a result of Rudnick over $ \mathbb{Q}$.


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Additional Information

Simon Marshall
Affiliation: School of Mathematics, The Institute for Advanced Study, Einstein Drive, Princeton, New Jersey 08540
Email: slm@math.princeton.edu

DOI: https://doi.org/10.1090/S0894-0347-2011-00700-5
Received by editor(s): July 1, 2010
Received by editor(s) in revised form: December 10, 2010, and February 22, 2011
Published electronically: April 6, 2011
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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