HYBRID MEAN VALUE OF THE GENERALIZED KLOOSTERMAN SUMS AND DIRICHLET CHARACTER OF POLYNOMIALS

A hybrid mean value involving a new Gauss sums and Dedekind sums

‎In this paper‎, ‎we introduce a new sum‎ ‎analogous to Gauss sum‎, ‎then we use the properties of the‎ ‎classical Gauss sums and analytic method to study the hybrid mean‎ ‎value problem involving this new sums and Dedekind sums‎, ‎and‎ ‎give an interesting identity for it.

The Value 4 of Binary Kloosterman Sums

Kloosterman sums have recently become the focus of much research, most notably due to their applications in cryptography and their relations to coding theory. Very recently Mesnager has showed that the value 4 of binary Kloosterman sums gives rise to several infinite classes of bent functions, hyper-bent functions and semi-bent functions in even dimension. In this paper we analyze the different...

Visual properties of generalized Kloosterman sums

For a positive integer m and a subgroup Λ of the unit group (Z/mZ)×, the corresponding generalized Kloosterman sum is the function K(a, b,m,Λ) = ∑ u∈Λ e( au+bu−1 m ). Unlike classical Kloosterman sums, which are real valued, generalized Kloosterman sums display a surprising array of visual features when their values are plotted in the complex plane. In a variety of instances, we identify the pr...

Second Moments of Dirichlet L-functions Weighted by Kloosterman Sums

Mean value theorems for long Dirichlet polynomials and tails of Dirichlet series

We obtain formulas for computing mean values of Dirichlet polynomials that have more terms than the length of the integration range. These formulas allow one to compute the contribution of off-diagonal terms provided one knows the correlation functions for the coefficients of the Dirichlet polynomials. A smooth weight is used to control error terms, and this weight can in typical applications b...