On the mean square of short exponential sums related to cusp forms

Mean square value of exponential sums related to representation of integers as sum of two squares

1. Introduction. The problem we address here arises in the study of the error function in the shifted circle problem (see [BCDL]). Let α = (α 1 , α 2) ∈ R

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...

A 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.

On Some Exponential Sums Related to the Coulter's Polynomial

In this paper, the formulas of some exponential sums over finite field, related to the Coulter’s polynomial, are settled based on the Coulter’s theorems on Weil sums, which may have potential application in the construction of linear codes with few weights.

On the Hybrid Mean Value of Cochrane Sums and Two-term Exponential Sums