On the fourth power mean of the generalized quadratic Gauss sums

The main purpose of this paper is to use elementary methods and properties of the classical Gauss sums to study the computational problem of one kind of fourth power mean of the generalized quadratic Gauss sums mod q (a positive odd number), and give an exact computational formula for it.     

On an identity associated with Weil's estimate and its applications

In this paper we study the fourth mean value of generalized quadratic Gauss sums, and get an interesting identity associated with Weil's estimate,

     

Gauss sums and multinomial coefficients

Consider a Gauss sum for a finite field of characteristic p, where p is an odd prime. When such a sum (or a product of such sums) is a p-adic integer we show how it can be realized as a p-adic limit of a sequence of multinomial coefficients. As an application we generalize some congruences of Hahn and Lee to exhibit p-adic limit formulae, in terms of multinomial coefficients, for certain algebraic integers in imaginary quadratic fields related to the splitting of rational primes. We also give an example illustrating how such congruences arise from a p-integral formal group law attached to the p-adic unit part of a product of Gauss sums.     

关于三次高斯和的均值

主要研究三次高斯和的均值性质，并给出一个较强的渐近公式。     

Incomplete higher-order Gauss sums

We consider the classical incomplete higher-order Gauss sums

     

Explicit multiplicative relations between Gauss sums

H. Hasse conjectured that all multiplicative relations between Gauss sums essentially follow from the Davenport-Hasse product formula and the norm relation for Gauss sums. While this is known to be false, very few counterexamples, now known as sign ambiguities, have been given. Here, we provide an explicit product formula giving an infinite class of new sign ambiguities and resolve the ambiguous sign in terms of the order of the ideal class of quadratic primes.     

关于特征和的混合均值

研究了特征和及其算术性质,并利用解析方法得到了两个关于特征和的混合均值的渐近公式,从而推广了特征和的算术性质。     

On some hybrid power moments of products of generalized quadratic Gauss sums and Kloosterman sums*

In this paper, we investigate hybrid power moments of generalized quadratic Gauss sums weighted with powers of Kloosterman sums and with powers of values of Dirichlet L-functions at 1. We obtain several exact formulas for prime and prime power modulus and some asymptotic formulas.     

广义k次Gauss和及其四次均值

本文研究了广义k次Gauss和的四次均值,给出了两个计算公式．     

On the mean value formula of dedekind sums

The main purpose of this paper is to use the mean value theorem of the Dirichlet L-function to study the distribution property of Dedekind sums, and to give a sharper mean value formula. This work is supported by the National Natural Science Foundation of P. R. China     

三次Gauss和及二项指数和的混合均值

我们用三角和的性质研究一类三次Gauss和与两项指数和混合均值的计算问题,并给出一个精确的计算公式.     

Moments of Generalized Quadratic Gauss Sums Weighted by L-Functions

The main purpose of this paper is using estimates for character sums and analytic methods to study the second, fourth, and sixth order moments of generalized quadratic Gauss sums weighted by L-functions. Three asymptotic formulae are obtained.     

Dirichlet characters,Gauss sums and arithmetic Fourier transforms

In this paper, a general algorithm for the computation of the Fourier coefficients of 2π-periodic(continuous) functions is developed based on Dirichlet characters, Gauss sums and the generalized M¨obius transform. It permits the direct extraction of the Fourier cosine and sine coefficients. Three special cases of our algorithm are presented. A VLSI architecture is presented and the error estimates are given.     

三次高斯和与Kloosterman和的线性递推公式

应用三角和方法以及高斯和的若干性质,研究三次高斯和与Kloosterman和的一类高次混合均值的计算问题,本文给出该混合均值的一个有趣的线性递推公式.同时,还应用该递推公式,得到三次高斯和与Kloosterman和的高次混合均值的一系列较强的渐近公式.     

两个不同Gauss和的混合均值

本文利用解析方法以及三角和的性质研究两个不同Gauss和的混合均值的计算问题,并给出一个精确的计算公式.作为我们结果的应用,得到了关于模p的一类对角同余方程解的个数的计算公式,其中p是一个奇素数.     

A hybrid mean value formula involving Kloosterman sums and Hurwitz zeta-function

The main purpose of this paper is using the mean value theorem of Dirichlet L-function and the estimates for character sums to study the asymptotic properties of a hybrid mean value of Kloosterman sums with the weight of Hurwitz zeta-function and the Cochrane sums, and give an interesting mean value formula for it.     

On hybrid mean value of Dedekind sums and two-term exponential sums

In this paper, we use the elementary and analytic methods to study the computational problem of one kind mean value involving the classical Dedekind sums and two-term exponential sums, and give two exact computational formulae for them.     

The First Power Mean of the Inversion of L-Functions Weighted by Quadratic Gauss Sums

The main purpose of this paper is to use estimates for character sums and analytic methods to study the first power mean of the inversion of Dirichlet L-functions with the weight of general quadratic Gauss sums, and three asymptotic formulae are obtained.     

关于Dirichlet L-函数的2k次加权均值

本文的主要目的是利用特征和估计及其三角和方法研究Dirichlet L-函数的2k次加权均值，并得到了一个较为精确的渐近公式。