On exponential sums involving Fourier coefficients of cusp forms
نویسندگان
چکیده
منابع مشابه
On Sums of Fourier Coefficients of Cusp Forms
in case f(n) is the Fourier coefficient of a holomorphic or non-holomorphic cusp form. We shall first deal with the latter case, which is more complicated. Let as usual {λj = κj + 14} ∪ {0} be the discrete spectrum of the non-Euclidean Laplacian acting on SL(2,Z) –automorphic forms. Further let ρj(n) denote the n-th Fourier coefficient of the Maass wave form φj(z) corresponding to the eigenvalu...
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We consider two problems concerning signs of Fourier coefficients of classical modular forms, or equivalently Hecke eigenvalues: first, we give an upper bound for the size of the first sign-change of Hecke eigenvalues in terms of conductor and weight; second, we investigate to what extent the signs of Fourier coefficients determine an unique modular form. In both cases we improve recent results...
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s=1/2 where E(z, s) is the Eisenstein series for SL2(Z). In general one tries to deduce good estimates for these sums assuming the parameters a, b, h are of considerable size. The additive divisor problem has an extensive history and we refer the reader to [1] for a short introduction. Let us just mention that in the special case a = b = 1 one can derive very sharp results by employing the spec...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2012
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2011.07.003