Effective forms of the Sato--Tate conjecture

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.

arXiv comment19 pages. The condition that the level be squarefree is removed

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Cited by in corpus (5)

• On the largest prime factor of non-zero Fourier coefficients of Hecke eigenforms
• A zero density estimate and fractional imaginary parts of zeros for ${\mathrm{GL}}_2$ $L$-functions
• Equidistribution of Kloosterman sums over function fields
• Exceptional zeros of Rankin-Selberg $L$-functions and joint Sato-Tate distributions
• Almost all primes satisfy the Atkin-Serre conjecture and are not extremal