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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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Effective equidistribution and property $(\tau )$
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by M. Einsiedler, G. Margulis, A. Mohammadi and A. Venkatesh HTML | PDF
J. Amer. Math. Soc. 33 (2020), 223-289 Request permission


We prove a quantitative equidistribution statement for adelic homogeneous subsets whose stabilizer is maximal and semisimple. Fixing the ambient space, the statement is uniform in all parameters.

We explain how this implies certain equidistribution theorems which, even in a qualitative form, are not accessible to measure-classification theorems. As another application, we describe another proof of property $(\tau )$ for arithmetic groups.

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Additional Information
  • M. Einsiedler
  • Affiliation: Departement Mathematik, ETH Zürich, Rämistrasse 101, 8092, Zürich, Switzerland
  • MR Author ID: 636562
  • Email:
  • G. Margulis
  • Affiliation: Department of Mathematics, Yale University, P.O. Box 208283, New Haven, Connecticut 06520-8283
  • MR Author ID: 196455
  • Email:
  • A. Mohammadi
  • Affiliation: Department of Mathematics, UC San Diego, 9500 Gilman Drive, La Jolla, California 92093
  • MR Author ID: 886399
  • Email:
  • A. Venkatesh
  • Affiliation: Department of Mathematics, Stanford University, Stanford, California 94305
  • MR Author ID: 693009
  • Email:
  • Received by editor(s): March 31, 2015
  • Received by editor(s) in revised form: August 28, 2017, October 21, 2018, and June 21, 2019
  • Published electronically: October 2, 2019
  • Additional Notes: The first author acknowledges support from the SNF (Grant 200021-127145 and 200021-152819)
    The second author acknowledges support from the NSF (Grant 1265695)
    The third author acknowledges support from the NSF and Alfred P. Sloan Research Fellowship
    The fourth author acknowledges support from the NSF and the Packard foundation
  • © Copyright 2019 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 33 (2020), 223-289
  • MSC (2010): Primary 11E99, 37A17, 37A45; Secondary 22E55
  • DOI:
  • MathSciNet review: 4066475