Triple correlation sums of coefficients of cusp forms
نویسندگان
چکیده
We produce nontrivial asymptotic estimates for shifted sums of the form ? a ( h ) b m c 2 ? , in which n are un-normalized Fourier coefficients holomorphic cusp forms. These results unconditional, but we demonstrate how to strengthen them under Riemann Hypothesis. As an application, show that there infinitely many three term arithmetic progressions + such ? 0 .
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...
متن کاملA Relation between Fourier Coefficients of Holomorphic Cusp Forms and Exponential Sums
We consider certain specific exponential sums related to holomorphic cusp forms, give a reformulation for the Lehmer conjecture and prove that certain exponential sums of Fourier coefficients of holomorphic cusp forms contain information on other similar non-overlapping exponential sums. Also, we prove an Omega result for short sums of Fourier coefficients.
متن کاملSums of Reciprocals of Triple Binomial Coefficients
Recommended by George Andrews We investigate the integral representation of infinite sums involving the reciprocals of triple bino-mial coefficients. We also recover some wellknown properties of ζ3 and extend the range of results given by other authors.
متن کاملFourier Coefficients of Hilbert Cusp Forms Associated with Mixed Hilbert Cusp Forms
We express the Fourier coefficients of the Hilbert cusp form Lhf associated with mixed Hilbert cusp forms f and h in terms of the Fourier coefficients of a certain periodic function determined by f and h. We also obtain an expression of each Fourier coefficient of Lhf as an infinite series involving the Fourier coefficients of f and h.
متن کاملOn signs of Fourier coefficients of cusp forms 209
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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2021
ISSN: ['0022-314X', '1096-1658']
DOI: https://doi.org/10.1016/j.jnt.2020.08.007