Some Density Results on Sets of Primes for Hecke Eigenvalues

Aiyue Zou, Huixue Lao, Shu Luo and Jie Wu

Journal of Mathematics, 2021, vol. 2021, 1-12

Abstract: Let f and g be two distinct holomorphic cusp forms for SL2ℤ, and we writeλfn and λgn for their corresponding Hecke eigenvalues. Firstly, we study the behavior of the signs of the sequences λfpλfpj for any even positive integer j. Moreover, we obtain the analytic density for the set of primes where the product λfpiλfpj is strictly less than λgpiλgpj. Finally, we investigate the distribution of linear combinations of λfpj and λgpj in a given interval. These results generalize previous ones.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:2462693

DOI: 10.1155/2021/2462693

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