关于超级Cochrane和的混合型均值

本文利用Gauss和与原特征的性质以及DirichletL-函数的均值定理研究了超级Cochrane和与超级Kloosterman和的混合型均值,并给出了一个有趣的渐近公式.     

A Generalization on the Difference Between an Integer and Its Inverse Modulo Q

The main purpose of this paper is to use the properties of the Gauss sums, primitive characters and the mean value of Dirichlet L-functions to study the hybrid mean value of the error term E（n, l, c, q） and the hyper-Kloosterman sums K（h,n＋1,q）, the asymptotic property of the mean square value ∑^p c=1 E^2（n, 1, c, p）, and give two interesting mean value formulae.     

A note on the Cochrane sum and its hybrid mean value formula

In this paper, we use the properties of Gauss sums, primitive characters and the mean value theorems of Dirichlet L-functions to study the hybrid mean value of Cochrane sums and general Kloosterman sums, and give two sharp asymptotic formulae.     

高次高斯和均值的精确计算公式

本文研究了高次高斯和的计算问题.利用指数和的相关性质及各种变换技巧与方法,获得了高次均值的一个精确计算公式,拓展了经典高斯和均值计算的结果.     

两项指数和及两项特征和的混合均值

利用解析方法以及高斯和的性质研究一类二项指数和及二项特征和的混合均值问题,并给出一个精确的表示式.作为应用,给出该和式的一个渐近公式以及该和式与Dirichlet L-函数加权均值的一个较强的渐近公式.     

On the Dedekind Sums and Two-Term Exponential Sums

In this paper, the authors use the analytic methods and the properties of character sums mod p to study the computational problem of one kind of mean value involving the classical Dedekind sums and two-term exponential sums, and give an exact computational formula for it.     

The mean value involving Dedekind sums and two-term exponential sums

In this paper,we use the analytic methods to study the mean value properties involving the classical Dedekind sums and two-term exponential sums,and give two sharper asymptotic formulae for it.     

Mean Value on the Difference Between a Quadratic Residue and Its Inverse Modulo p

The main purpose of this paper is to use the generalized Bernoulli numbers, Gauss sums and the mean value theorems of Dirichlet L-functions between a quadratic residue and its inverse modulo p value formula. to study the asymptotic property of the difference （a prime）, and to give an interesting hybrid mean     

Gauss和与广义Kloosterman和的几个新的恒等式

主要应用Gauss和的性质和解析方法来研究Gauss和与广义Kloosterman和之间的关系,并且给出了几个有趣的恒等式.     

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.     

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。     

关于广义$k$次高斯和的均值

The main purpose of this paper is using residue system and character sums methods to investigate the mean value properties of general k-th Gauss sums,and two exact calculating formulas are given.     

On the mean value of

Let χ be the Dirichlet character modulo q3 and L(s,χ) denote the corresponding Dirichlet L-function. The mean value of is studied and a few asymptotic formulae are given. Hybrid mean value of , general Kloosterman sums and general quadratic Gauss sums are considered.     

On Cochrane sums over short intervals

The main purpose of this paper is to study the mean square value problem of Cochrane sums over short intervals by using the properties of Gauss sums and Kloosterman sums, and finally give a sharp asymptotic formula.     

Wittmann's Law of Iterated Logarithm for Tail Sums of B-Valued Random Variables

We present an analogue of Wittmann's law of iterated logarithm (LIL) for tail sums of independent B-valued random variables by using the isoperimetric method and give the precise value of the upper limit for the LIL for tail sums.     

A hybrid mean value related to the Dedekind sums and Kloosterman sums

The main purpose of this paper is to use the properties of character sum and the analytic method to study a hybrid mean value problem related to the Dedekind sums and Kloosterman sums, and give some interesting mean value formulae and identities for it.     

关于Fermat素数与L-函数的加权均值

本文研究了一类以Fermat素数为模的Dirichlet L-函数加权均值的计算问题. 利用初等方法以及Dirichlet 和的性质, 获得了一个有趣的计算公式.     

On the 2<Emphasis Type="Italic">k</Emphasis>-th Power Mean of Inversion of <Emphasis Type="Italic">L</Emphasis>-functions with the Weight of the Gauss Sum

Abstract The main purpose of this paper is to use the estimate for character sums and the method of trigonometric sums to study the 2k-th power mean of the inversion of Dirichlet L-functions with the weight of the Gauss sums, and give a sharper asymptotic formula. This work is supported by the Doctorate Foundation of Xi’an Jiaotong University     

On certain character sums over p ‐adic rings and their L ‐functions

In this paper we present a new method for evaluating exponential sums associated to a restricted power series in one variable modulo p^l , a power of a prime. We show that for sufficiently large l, these sums can be expressed in terms of Gauss sums. Moreover, we study the associated L ‐functions; we show that they are rational, then we determine their degrees and the weights as Weil numbers of their reciprocal roots and poles. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

r次剩余及其关于模p的逆之差的混合均值

利用广义Bernoulli数,Gauss和与Dirichlet L-函数的均值来研究r次剩余及其关于模p的逆之差,并给出与广义Kloosterman和相关的一些混合均值公式.