广义Bernoulli数和广义高阶Bernoulli数

定义了广义Bernoulli数和广义高阶Bernoulli数，建立了它们的递推公式和有关性质，从而推广了Bernoulli数和高阶Bernoulli数。     

关于广义齐性Cochrane和的加权均值

研究了广义齐性Cochrane和的一些加权均值,并利用不完全区间上特征和的性质,Dirichlet函数的均值估计以及周期Bernoulli多项式的性质,得到一些较强的渐近公式．     

广义n阶Euler-Bernoulli多项式

本文得到了广义n阶Euler数和广义n阶Bernoulli数,广义n阶Euler多项式和广义n阶Bernoulli多项式的关系式。     

广义二次Gauss和与广义Kloosterman和的混合均值

利用分析的方法及经典二次Gauss和的性质,研究了一类广义二次Gauss和与广义Kloosterman和的混合均值的计算问题,并得到了一个精确的计算公式.     

广义m阶Bernoulli数和广义m阶Euler数的计算公式

使用发生函数方法,利用第一类Stirling数和第二类Stirling数分别给出广义m阶Bernoulli数和广义m阶Euler数的计算公式.     

关于广义Dedekind和的加权均值

利用Dirichlet L－函数的均值定理和特征和估计，研究了广义Dedekind和与HurwitzZeta-函数的加权均值分布性质，并给出一个有趣的渐近公式。     

关于广义Dedekind和的2k次均值

本文利用 Ｄｉｒｉｃｈｌｅｔ Ｌ－函数的均值定理,研究广义 Ｄｅｄｅｋｉｎｄ和的渐近性质,并给出一个有趣的渐近公式．     

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.     

关于广义Kloosterman和的高次均值的一个注记

本文的主要目的是利用三次特征的性质,以及W.Duke,H.Iwaniec,B.J Birch等人的重要工作来研究广义Kloosterman和的高次均值,并给出一些有趣的计算公式.     

关于广义Kloosterman和的高次均值的一个注记

本文的主要目的是利用三次特征的性质,以及W.Duke,H.Iwaniec,B.J.Birch等人的重要工作来研究广义Kloosterman和的高次均值,并给出一些有趣的计算公式.     

Degenerate Bernoulli polynomials, generalized factorial sums, and their applications

We prove a general symmetric identity involving the degenerate Bernoulli polynomials and sums of generalized falling factorials, which unifies several known identities for Bernoulli and degenerate Bernoulli numbers and polynomials. We use this identity to describe some combinatorial relations between these polynomials and generalized factorial sums. As further applications we derive several identities, recurrences, and congruences involving the Bernoulli numbers, degenerate Bernoulli numbers, generalized factorial sums, Stirling numbers of the first kind, Bernoulli numbers of higher order, and Bernoulli numbers of the second kind.     

General Kloosterman Sums and the Difference Between an Integer and Its Inverse Modulo Q

The main purpose of this paper is to use the generalized Bernoulli numbers, Gauss sums and the mean value theorems of Dirichlet L-functions to study the asymptotic property of one class of number-theoretic functions, and to give four interesting hybrid mean value formulae.     

Sums of products of Cauchy numbers

In this paper, we consider a kind of sums involving Cauchy numbers, which have not been studied in the literature. By means of the method of coefficients, we give some properties of the sums. We further derive some recurrence relations and establish a series of identities involving the sums, Stirling numbers, generalized Bernoulli numbers, generalized Euler numbers, Lah numbers, and harmonic numbers. In particular, we generalize some relations between two kinds of Cauchy numbers and some identities for Cauchy numbers and Stirling numbers.     

Generalized Dedekind symbols associated with the Eisenstein series

We have shown recently that the space of modular forms, the space of generalized Dedekind sums, and the space of period polynomials are all isomorphic. In this paper, we will prove, under these isomorphisms, that the Eisenstein series correspond to the Apostol generalized Dedekind sums, and that the period polynomials are expressed in terms of Bernoulli numbers. This gives us a new more natural proof of the reciprocity law for the Apostol generalized Dedekind sums. Our proof yields as a by-product new polylogarithm identities.

     

关于广义三项指数和的四次均值

本文利用三角和等式以及既约剩余系的性质, 研究了广义三项指数和的四次均值的计算问题, 并给出了特定情形下的一些等式.     

广义对角多项式指数和的估计

利用高斯和与次数矩阵Smith标准形的不变因子,给出了有限域上广义对角多项式指数和的估计,从而改进了Deligne-Weil型估计这类多项式指数和的结果.     

Mean Value of Kloosterman Sums over Short Intervals

This paper is concerned with a kind of mean value problem of Kloosterman sums, which will lead to a sum of Kloosterman sums over short intervals.     

Sums of products of hypergeometric Bernoulli numbers

We give a formula for sums of products of hypergeometric Bernoulli numbers. This formula is proved by using special values of multiple analogues of hypergeometric zeta functions.     

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