Signs of Fourier coefficients of cusp form at sum of two squares

Abstract

In this article, we investigate the sign changes of the sequence of coefficients at sum of two squares where the coefficients are the Fourier coefficients of the normalized Hecke eigen cusp form for the full modular group. We provide the quantitative result for the number of sign changes of the sequence in a small interval.

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Correspondence to Manish Kumar Pandey.

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Communicating Editor: Sanoli Gun

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Banerjee, S., Pandey, M.K. Signs of Fourier coefficients of cusp form at sum of two squares. Proc Math Sci 130, 2 (2020). https://doi.org/10.1007/s12044-019-0534-4

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Keywords

  • Cusp form
  • Fourier coefficients
  • sign change
  • asymptotic behaviour
  • Rankin–Selberg L-function

Mathematics Subject Classification

  • Primary: 11F11
  • 11F30
  • 11M06
  • Secondary: 11N37