منابع مشابه
The Distribution of the Eigenvalues of Hecke Operators
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)...
متن کاملSign Changes of Hecke Eigenvalues
in the Maass case. In [14] Kowalski, Lau, Soundararajan and Wu investigate the problem of the first sign change of λf (n) for holomorphic f . They remark on the similarities with the problem of the least quadratic residue. This motivates the point of view that the signs of λf (n) are GL(2) analogues of real characters. The frequency of signs and sign changes and other related questions have bee...
متن کاملOn Bounding Hecke-siegel Eigenvalues
We use the action of the Hecke operators T̃j(p 2) (1 ≤ j ≤ n) on the Fourier coefficients of Siegel modular forms to bound the eigenvalues of these Hecke operators. This extends work of Duke-Howe-Li and of Kohnen, who provided bounds on the eigenvalues of the operator T (p).
متن کاملEffective equidistribution of eigenvalues of Hecke operators
Article history: Received 13 October 2007 Revised 9 May 2008 Available online 17 December 2008 Communicated by David Goss 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...
متن کاملSums of Hecke Eigenvalues over Quadratic Polynomials
Let f(z) = P n a(n)n e(nz) ∈ Sk(N,χ) be a cusp form for Γ0(N), weight k > 4 and character χ. Let q(x) = x + sx+ t ∈ Z[x] be a quadratic polynomial. It is shown that
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2006
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-06-08709-0