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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Mass equidistribution for automorphic forms of cohomological type on $GL_2$
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by Simon Marshall PDF
J. Amer. Math. Soc. 24 (2011), 1051-1103 Request permission

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
  • 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
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • 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
  • MathSciNet review: 2813338