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The distribution of the eigenvalues of Hecke operators

J. Brian Conrey·William Duke·David W. Farmer
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Abstract

For each prime $p$, we determine the distribution of the $p^{th}$ Fourier coefficients of the Hecke eigenforms of large weight for the full modular group. As $p\to\infty$, this distribution tends to the Sato--Tate distribution.

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J. Brian Conrey, William Duke, David W. Farmer. 1996-09-10. The distribution of the eigenvalues of Hecke operators. https://arxiv.org/abs/math/9609214

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