Distribution of Hecke eigenvalues

Nagoshi, Hirofumi

doi:10.1090/S0002-9939-06-08709-0

Distribution of Hecke eigenvalues
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Proc. Amer. Math. Soc. 134 (2006), 3097-3106 Request permission

Abstract:

We give two results concerning the distribution of Hecke eigenvalues of $SL(2, \mathbb {Z})$. The first result asserts that on certain average the Sato-Tate conjecture holds. The second result deals with the Gaussian central limit theorem for Hecke eigenvalues.

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