Asymptotic Fourier Coefficients for a C∞ Bell (Smoothed-“Top-Hat”) & the Fourier Extension Problem

Asymptotic Relations among Fourier Coefficients of Real-analytic Eisenstein Series

Following Wolpert, we find a set of asymptotic relations among the Fourier coefficients of real-analytic Eisenstein series. The relations are found by evaluating the integral of the product of an Eisenstein series φir with an exponential factor along a horocycle. We evaluate the integral in two ways by exploiting the automorphicity of φir ; the first of these evaluations immediately gives us on...

Quadrature formulas for Fourier coefficients

Quadrature formulae for Fourier coefficients

We consider quadrature formulas of high degree of precision for the computation of the Fourier coefficients in expansions of functions with respect to a system of orthogonal polynomials. In particular, we show the uniqueness of a multiple node formula for the Fourier-Tchebycheff coefficients given by Michhelli and Sharma and construct new Gaussian formulas for the Fourier coefficients of a func...

Transformations of Fourier Coefficients

Introduction. In 1923 M. Fekete [2]2 introduced the concept of factor sequences that left invariant the class of a Fourier series. That is, Fekete investigated the conditions to which a sequence of constants (X„) must be subjected in order that (X„a„, X„i„) be Fourier coefficients of a function of the same class, K, as that of the function determined by (an, bn). Whenever (X„) has this property...

An Additive Problem in the Fourier Coefficients of Cusp Forms

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...