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Comparing Hecke eigenvalues of newforms

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Abstract

Given two distinct newforms with real Fourier coefficients, we show that the set of primes where the Hecke eigenvalues of one of them dominate the Hecke eigenvalues of the other has density \(\ge \)1/16. Furthermore, if the two newforms do not have complex multiplication, and neither is a quadratic twist of the other, we also prove a similar result for the squares of their Hecke eigenvalues.

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Acknowledgements

The author thanks Farshid Hajir, Dinakar Ramakrishnan, and Siman Wong for helpful conversations, and also the anonymous referee for useful comments and suggestions.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Massachusetts Amherst, 710 N Pleasant St, Amherst, MA, 01003, USA

    Liubomir Chiriac

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  1. Liubomir Chiriac
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Correspondence to Liubomir Chiriac.

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Chiriac, L. Comparing Hecke eigenvalues of newforms. Arch. Math. 109, 223–229 (2017). https://doi.org/10.1007/s00013-017-1072-x

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  • DOI: https://doi.org/10.1007/s00013-017-1072-x

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