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Proceedings of the American Mathematical Society

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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

Abstract:

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: zarghani@math.uni-duesseldorf.de, zarghani.s@gmail.com
  • 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: https://doi.org/10.1090/S0002-9939-2011-10807-4
  • MathSciNet review: 2823032