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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Hecke operators for non-congruence subgroups of Bianchi groups
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by Saeid Hamzeh Zarghani PDF
Proc. Amer. Math. Soc. 139 (2011), 3853-3865 Request permission


We prove that the action of the Hecke operators on the cohomology of a finite index non-congruence subgroup $\Gamma$ of a Bianchi group is essentially the same as the action of Hecke operators on the cohomology groups of $\hat {\Gamma }$, the congruence closure of $\Gamma$. This is a generalization of Atkin’s conjecture, first confirmed in a special case by Serre in $1987$ and proved in general by Berger in $1994$.
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Additional Information
  • Saeid Hamzeh Zarghani
  • Affiliation: Department of Mathematics, Heinrich-Heine University Düsseldorf, Düsseldorf, Germany
  • Email:,
  • Received by editor(s): May 13, 2010
  • Received by editor(s) in revised form: September 21, 2010
  • Published electronically: March 25, 2011
  • Additional Notes: The author was supported in part by Graduirtenkolleg Homotopie und Kohomologie (GRK1150)

  • Dedicated: Before the first draft of this work was completed, Fritz Grunewald tragically passed away. Indeed, without his guidance and support this work would never have been done. I dedicate this paper to his memory with admiration, gratitude and love.
  • Communicated by: Kathrin Bringmann
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 139 (2011), 3853-3865
  • MSC (2010): Primary 11F03, 11F25, 11F75, 20G30; Secondary 19B37
  • DOI:
  • MathSciNet review: 2823032