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Some remarks related to Maeda's conjecture

Authors: M. Ram Murty and K. Srinivas
Journal: Proc. Amer. Math. Soc. 144 (2016), 4687-4692
MSC (2010): Primary 11F30; Secondary 11L07
Published electronically: April 27, 2016
MathSciNet review: 3544520
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Abstract: In this article we deal with the problem of counting the number of pairs of normalized eigenforms $ (f,g) $ of weight $ k$ and level $ N$ such that $ a_p (f) = a_p (g) $ where $ a_p (f) $ denotes the $ p$-th Fourier coefficient of $ f$. Here $ p$ is a fixed prime.

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  • [1] Jonathan M. Borwein and Robert M. Corless, Emerging tools for experimental mathematics, Amer. Math. Monthly 106 (1999), no. 10, 889-909. MR 1732501,
  • [2] Pierre Deligne, La conjecture de Weil. I, Inst. Hautes Études Sci. Publ. Math. 43 (1974), 273-307 (French). MR 0340258
  • [3] Haruzo Hida and Yoshitaka Maeda, Non-abelian base change for totally real fields, Pacific J. Math. Special Issue (1997), 189-217. Olga Taussky-Todd: in memoriam. MR 1610859,
  • [4] M. Ram Murty and Kaneenika Sinha, Effective equidistribution of eigenvalues of Hecke operators, J. Number Theory 129 (2009), no. 3, 681-714. MR 2488597,
  • [5] Panagiotis Tsaknias, A possible generalization of Maeda's conjecture, Computations with modular forms, Contrib. Math. Comput. Sci., vol. 6, Springer, Cham, 2014, pp. 317-329. MR 3381458,
  • [6] Jean-Pierre Serre, Répartition asymptotique des valeurs propres de l'opérateur de Hecke $ T_p$, J. Amer. Math. Soc. 10 (1997), no. 1, 75-102 (French). MR 1396897,
  • [7] J. D. Vaaler, Some extremal functions in Fourier analysis, Bull. Amer. Math. (2) 141 (3) (1995) 443-551.

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Additional Information

M. Ram Murty
Affiliation: Department of Mathematics and Statistics, Queen’s University, Jeffery Hall, 99 University Avenue, Kingston, Ontario, Cananda K7L 3N6

K. Srinivas
Affiliation: The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai, 600 113, Tamilnadu, India

Keywords: Maeda conjecture, equidistribution, Hecke eigenvalues
Received by editor(s): July 21, 2015
Received by editor(s) in revised form: January 27, 2016
Published electronically: April 27, 2016
Additional Notes: Research of the first author was partially supported by an NSERC Discovery grant.
Communicated by: Matthew A. Papanikolas
Article copyright: © Copyright 2016 American Mathematical Society

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