The Distribution of the Eigenvalues of Hecke Operators
نویسندگان
چکیده
τ(n)e(nz). The two equations were proven for τ(n) by Mordell, using what are now known as the Hecke operators. The inequality was proven by Deligne as a consequence of his proof of the Weil conjectures. Those results determine everything about af (n) except for the distribution of the af (p) ∈ [−2, 2]. Define θf (p) ∈ [0, π] by af (p) = 2 cos θf (p). It is conjectured that for each f the θf (p) are uniformly distributed with respect to the Sato–Tate measure
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