Fourier coefficients and Hecke eigenvalues
نویسندگان
چکیده
منابع مشابه
Fourier Coefficients of Hecke Eigenforms
We provide systematic evaluations, in terms of binary quadratic representations of 4p, for the p-th Fourier coefficients of each member f of an infinite class C of CM eigenforms. As an application, previously conjectured evaluations of three algebro-geometric character sums can now be formulated explicitly without reference to eigenforms. There are several non-CM newforms that appear to share s...
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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...
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We sharpen some estimates of Rankin on power sums of Hecke eigenvalues, by using Kim & Shahidi’s recent results on higher order symmetric powers. As an application, we improve Kohnen, Lau & Shparlinski’s lower bound for the number of Hecke eigenvalues of same signs.
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: Nagoya Mathematical Journal
سال: 1998
ISSN: 0027-7630,2152-6842
DOI: 10.1017/s0027763000006565