Oscillatory behavior and equidistribution of signs of Fourier coefficients of cusp forms

Abstract

In this paper, we discuss questions related to the oscillatory behavior and the equidistribution of signs for certain subfamilies of Fourier coefficients of integral weight newforms with a non-trivial nebentypus as well as Fourier coefficients of eigenforms of half-integral weight reachable by the Shimura correspondence.

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Acknowledgements

The author is greatly grateful to Francesc Fité for a helpful conversation. He also wishes to thank Gabor Wiese for his valuable comments on the first draft of this work as well as Ilker Inam for providing him with some data for numerical experiments. Thanks are also due to the referee for his careful reading and their helpful comments which improved the paper.

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Correspondence to Mohammed Amin Amri.

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Amri, M.A. Oscillatory behavior and equidistribution of signs of Fourier coefficients of cusp forms. Ramanujan J 50, 505–526 (2019). https://doi.org/10.1007/s11139-018-0078-8

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Keywords

  • Sign changes
  • Fourier coefficients of cusp forms
  • Sato–Tate equidistribution

Mathematics Subject Classification

  • 11F03
  • 11F30
  • 11F37