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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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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Sign changes of Hecke eigenvalues of Siegel cusp forms of degree $2$
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by Ameya Pitale and Ralf Schmidt PDF
Proc. Amer. Math. Soc. 136 (2008), 3831-3838 Request permission

Abstract:

Let $\mu (n)$, $n>0$, be the sequence of Hecke eigenvalues of a cuspidal Siegel eigenform $F$ of degree $2$. It is proved that if $F$ is not in the Maaß space, then there exist infinitely many primes $p$ for which the sequence $\mu (p^r)$, $r>0$, has infinitely many sign changes.
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Additional Information
  • Ameya Pitale
  • Affiliation: Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019
  • MR Author ID: 778555
  • Email: ameya@math.ou.edu
  • Ralf Schmidt
  • Affiliation: Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019
  • MR Author ID: 636524
  • Email: rschmidt@math.ou.edu
  • Received by editor(s): May 15, 2007
  • Received by editor(s) in revised form: October 2, 2007
  • Published electronically: June 2, 2008
  • Communicated by: Ken Ono
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 136 (2008), 3831-3838
  • MSC (2000): Primary 11F46
  • DOI: https://doi.org/10.1090/S0002-9939-08-09364-7
  • MathSciNet review: 2425722