Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

Request Permissions   Purchase Content 
 

 

Distinguishing Hecke eigenforms


Authors: M. Ram Murty and Sudhir Pujahari
Journal: Proc. Amer. Math. Soc. 145 (2017), 1899-1904
MSC (2010): Primary 11F11, 11F12, 11F30
DOI: https://doi.org/10.1090/proc/13446
Published electronically: November 3, 2016
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 11F11, 11F12, 11F30

Retrieve articles in all journals with MSC (2010): 11F11, 11F12, 11F30


Additional Information

M. Ram Murty
Affiliation: Department of Mathematics and Statistics, Queen’s University, Kingston, Ontario, Canada K7L 3N6
Email: murty@mast.queensu.ca

Sudhir Pujahari
Affiliation: Department of Mathematics, Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019, India
Email: sudhirpujahari@hri.res.in

DOI: https://doi.org/10.1090/proc/13446
Keywords: Hecke eigenforms, Sato-Tate distribution, symmetric power $L$-functions
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
Article copyright: © Copyright 2016 American Mathematical Society