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Effective forms of the Sato–Tate conjecture

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Abstract

We prove effective forms of the Sato–Tate conjecture for holomorphic cuspidal newforms which improve on the author’s previous work (solo and joint with Lemke Oliver). We also prove an effective form of the joint Sato–Tate distribution for two twist-inequivalent newforms. Our results are unconditional because of recent work of Newton and Thorne.

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Acknowledgements

I thank Maksym Radziwiłł, Jeremy Rouse, Jack Thorne, John Voight, and Peng-Jie Wong for helpful discussions and the anonymous referees.

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  1. Department of Mathematics, University of Illinois, Urbana, IL, 61801, USA

    Jesse Thorner

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Correspondence to Jesse Thorner.

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Thorner, J. Effective forms of the Sato–Tate conjecture. Res Math Sci 8, 4 (2021). https://doi.org/10.1007/s40687-020-00234-3

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