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.     

指数和与特征和的混合均值

本文利用三角和估计及其特征和的性质研究一类二项指数和与多项式特征和的混合均值的计算问题,并给出两个有趣的计算公式.     

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.     

多项式的特征和与二项指数和的混合均值

本文主要利用解析方法以及二项指数和与Dirichlet特征的性质，研究多项式的特征和与二项三次指数和的混合均值的计算问题，并得到一个较强的渐近公式.     

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 Character Sum of Polynomials and the Two-term Exponential Sums

The main purpose of this paper is using the analytic method and the properties of the character sums to study the computational problem of one kind hybrid power mean involving the character sums of polynomials and the two-term exponential sums,and give several interesting identities and asymptotic formulae for them.     

多项式的特征和及其L-函数

本文使用解析方法及特征和的性质研究了一类多项式的特征和与模p的狄利克莱L-函数的混合幂均值的计算问题,并给出了它们的一些计算公式.     

Estimating Additive Character Sums for Fuchsian Groups

In the usual construction of non-holomorphic Eisenstein series, for a general Fuchsian group, a multiplicative character may be included. The properties of these series are well known. Here we instead include an additive character and develop the properties of the resulting series. We pay particular attention to additive characters that are non-cuspidal, i.e., that are not zero on some parabolic generators. These series may be used to estimate certain additive character sums. For example, asymptotics for a weighted sum over group elements that counts the number of appearances of a fixed generator of the Fuchsian group are obtained.     

广义Dedekind和与Hardy和

本文给出了广义Dedekind和与Hardy和的定义,研究了广义Dedekind和的算术性质,并把Hardy和表示成广义Dedekind和的形式．提出了广义Subrahmanyam等式和Knopp定理,并给出了证明．     

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.     

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。     

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.     

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.     

Dedekind和的一个性质

Ｄｅｄｅｋｉｎｄ和的Ｋｎｏｐｐ等式是与Ｈｅｃｋｅ算子有关的一个算术性质，本文不借助ｅｔａ－函数的概念，给予Ｋｎｏｐｐ等式的一个简短的初等证明，同时把Ｋｎｏｐｐ等式拓广到广义Ｄｅｄｅｋｉｎｄ和中。     

两个新的mock theta双重和

最近, 张和李使用一个Bailey对, 获得了五个与$q$-超几何双重和相关的mock theta 函数. 本文使用此Bailey对, 我们进一步地建立了两个新的与Appell-Lerch和及theta级数相关的mock theta双重和. 进而也获得了其中一个新的mock theta函数和经典mock theta函数之间的一些关系式.     

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.     

关于Brewer和的一个有趣恒等式

主要目的是利用初等方法研究Brewer和的性质,并给出一个有趣的恒等式.     

位数码之和的幂的平均阶(I)

在本文中，我们给出了位数码之和的幂的平均阶的一个渐近公式．     

Conjugacy Classes,Class Sums and Character Tables for Hopf Algebras

We extend the notion of conjugacy classes and class sums from finite groups to semisimple Hopf algebras and show that the conjugacy classes are obtained from the factorization of H as irreducible left D(H)-modules. For quasitriangular semisimple Hopf algebras H, we prove that the product of two class sums is an integral combination of the class sums up to d ^?2 where d = dim H. We show also that in this case the character table is obtained from the S-matrix associated to D(H). Finally, we calculate explicitly the generalized character table of D(kS ₃), which is not a character table for any group. It moreover provides an example of a product of two class sums which is not an integral combination of class sums.     

Exponential Sums and Coding Theory: A Review

This article is a survey of several recent applications of methods from analytic number theory to research in coding theory, including results on Kloosterman codes, binary Goppa codes, and prime phase shift sequences. The mathematical methods focus on exponential sums, in particular Kloosterman sums. The interrelationships with the Weil–Carlitz–Uchiyama bound, results on Hecke operators, theorems of Bombieri and Deligne and the Eichler–Selberg trace formula are reviewed.