Triple correlations of 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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Let f be an elliptic cusp form of integral weight k on a congruence subgroup of Γ1 := SL2(Z) with real Fourier coefficients a(n)(n ≥ 1). Let r be a fixed positive integer. Then it was proved in [5] that the sequence (a(n)a(n + r))n≥1 has infinitely many nonnegative as well as infinitely many non-positive terms. The proof essentially is based on a sign-change result for the Fourier coefficients ...
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ژورنال
عنوان ژورنال: The Ramanujan Journal
سال: 2017
ISSN: 1382-4090,1572-9303
DOI: 10.1007/s11139-016-9874-1