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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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Distinguishing Hecke eigenforms
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by M. Ram Murty and Sudhir Pujahari PDF
Proc. Amer. Math. Soc. 145 (2017), 1899-1904 Request permission

Abstract:

Let $f_1, f_2$ be two distinct normalized Hecke eigenforms of weights $k_1$ and $k_2$ with at least one of them not of CM type and with $p$-th Hecke eigenvalues given by $a_p(f_1)p^{(k_1-1)/2}$ and $a_p(f_2) p^{(k_2-1)/2}$ respectively and $p$ being prime. If $a_p(f_1) = a_p(f_2)$ for a set of primes with positive upper density, then we show that $f_1 = f_2 \otimes \chi$ for some Dirichlet character $\chi$.
References
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Additional Information
  • M. Ram Murty
  • Affiliation: Department of Mathematics and Statistics, Queen’s University, Kingston, Ontario, Canada K7L 3N6
  • MR Author ID: 128555
  • Email: murty@mast.queensu.ca
  • Sudhir Pujahari
  • Affiliation: Department of Mathematics, Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India
  • MR Author ID: 1101430
  • Email: sudhirpujahari@hri.res.in
  • Received by editor(s): March 17, 2016
  • Received by editor(s) in revised form: June 1, 2016, and June 29, 2016
  • Published electronically: November 3, 2016
  • Additional Notes: The research of the first author was partially supported by an NSERC Discovery grant.
    The research of the second author was supported by a research fellowship from the Council of Scientific and Industrial Research (CSIR)
  • Communicated by: Matthew A. Papanikolas
  • © Copyright 2016 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 145 (2017), 1899-1904
  • MSC (2010): Primary 11F11, 11F12, 11F30
  • DOI: https://doi.org/10.1090/proc/13446
  • MathSciNet review: 3611306