The distribution of the eigenvalues of Hecke operators
classification
🧮 math.NT
keywords
distributionheckecoefficientsdetermineeigenformseigenvaluesfourierfull
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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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