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- W2026022015 abstract "In 1997, Serre proved an equidistribution theorem for eigenvalues of Hecke operators on the space S(N,k) of cusp forms of weight k and level N. In this paper, we derive an effective version of Serre's theorem. As a consequence, we estimate, for a given d and prime p coprime to N, the number of eigenvalues of the pth Hecke operator Tp acting on S(N,k) of degree less than or equal to d. This allows us to determine an effectively computable constant Bd such that if J0(N) is isogenous to a product of Q-simple abelian varieties of dimensions less than or equal to d, then N⩽Bd. We also study the effective equidistribution of eigenvalues of Frobenius acting on a family of curves over a fixed finite field as well as the eigenvalue distribution of adjacency matrices of families of regular graphs. These results are derived from a general “all-purpose” equidistribution theorem." @default.
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- W2026022015 date "2009-03-01" @default.
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- W2026022015 title "Effective equidistribution of eigenvalues of Hecke operators" @default.
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- W2026022015 doi "https://doi.org/10.1016/j.jnt.2008.10.010" @default.
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