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