The Ramanujan Journal

, Volume 50, Issue 3, pp 505–526 | Cite as

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

  • Mohammed Amin AmriEmail author


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.


Sign changes Fourier coefficients of cusp forms Sato–Tate equidistribution 

Mathematics Subject Classification

11F03 11F30 11F37 



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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Authors and Affiliations

  1. 1.ACSA Laboratory Department of Mathematics, Faculty of SciencesMohammed First UniversityOujdaMorocco

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