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Some Density Results on Sets of Primes for Hecke Eigenvalues

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  • Aiyue Zou
  • Huixue Lao
  • Shu Luo
  • Jie Wu

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.

Suggested Citation

  • Aiyue Zou & Huixue Lao & Shu Luo & Jie Wu, 2021. "Some Density Results on Sets of Primes for Hecke Eigenvalues," Journal of Mathematics, Hindawi, vol. 2021, pages 1-12, July.
    • Handle: RePEc:hin:jjmath:2462693
    DOI: 10.1155/2021/2462693
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