一般项趋于零且部分和有界的发散级数

构造一个发散的任意项无穷级数,该级数的一般项趋于零且部分和数列有界.     

Dirichlet L-函数倒数的2k次加权均值

本文主要目的是利用经典的Ｋｌｏｏｓｔｅｒｍａｎｎ和估计及其解析方法研究Ｄｉｒｉｃｈ－ｌｅｔ Ｌ-函数倒数的 ２ｋ次加权均值,得到了一个较为精确的渐近公式．     

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．     

Estimates for Sums of Coefficients of Dirichlet Series with Functional Equation

Suppose we have a Dirichlet series L(s) = _{n = 1} a _n n ^–s such that it, and its twists by Dirichlet characters have analytic continuation and a functional equation of a specific kind. Suppose also that the root numbers of the twists are equidistributed on the unit circle. The purpose of this note is to get an estimate for the quantity for a prime modulus p.We use a modification of the method of Chandrasekharan and Narasimhan and we use in an essential way a Rankin-Selberg type estimate for the average of |a _n|².     

On some Diophantine fourier series

We continue our study on arithmetical Fourier series by considering two Fourier series which are related to Diophantine analysis. The first one was studied by Hardy and Littlewood in connection with the classification of numbers and the second one was studied by Hartman and Wintner by Lebesgue integration theory.     

复指数Dirichlet 级数表示的整函数

该文对一个由复指数Dirichlet 级数表示的，其系数满足一给定增长条件且在一固定水平带形有界不恒为零的整函数的存在性， 给出了充分必要条件。     

Log-Polynomial Period Functions for Hecke Groups

In this article we shall determine the automorphic integrals of positive and negative integral weight associated with the full modular group and some Hecke groups. This will be done by using the Hecke Correspondence. We will also give a characterization of multiplier systems of real weight for Hecke groups.     

Kloosterman和的角度

有限域 Ｆｑ（ｑ为奇）上的 Ｋｌｏｏｓｔｅｒｍａｎ和是两个模为 ｑ１／２的共轭复数之和．这个复数的角度就称为相应的Ｋｌｏｏｓｔｅｒｍａｎ和的角度．我们在本文给出了Ｋｌｏｏｓｔｅｒｍａｎ和的角度的一些结果,改进了Ｋａｔｚ Ｎ．［１］的一些结果,也改进和推广了Ｃｏｎｒｅｙ　Ｊ．和Ｉｗａｎｉｅ Ｈ．［２］的结果．     

Dirichlet级数表示的整函数的增长性

本文系统地研究了在全平面上收敛的Dirichlet级数的增长性,得到了级数的系数和增长级之间关系的一系列充要条件．     

Hybrid Mean Value of the Hyper Cochrane Sums

The main purpose of this paper is to use the analytic methods to study the hybrid mean value involving the hyper Cochrane sums, and give several sharp asymptotic formulae.     

广义高阶Bernoulli数,Gauss和及广义Kloosterman和(英文)

利用广义高阶Bernoulli数的性质及Dirichlet L-函数的均值定理,研究了Gauss和及广义Kloosterman和与广义高阶Bernoulli数的均值性质,并给出两个有趣的渐近公式.     

A Joint Discrete Limit Theorem in the Space of Meromorphic Functions for General Dirichlet Series

A joint discrete limit theorem in the sense of the weak convergence of probability measures in the space of meromorphic functions for general Dirichlet series is proved.     

关于多元幂级数

引入了多元函数项级数的概念,给出了其收敛域及和函数的定义;通过详实的例子讨论了多元幂级数的收敛域、和函数及多元函数展开为多元幂级数的计算方法.     

On Dirichlet Series for Sums of Squares

Hardy and Wright (An Introduction to the Theory of Numbers, 5th edn., Oxford, 1979) recorded elegant closed forms for the generating functions of the divisor functions _k (n) and _k ²(n) in the terms of Riemann Zeta function (s) only. In this paper, we explore other arithmetical functions enjoying this remarkable property. In Theorem 2.1 below, we are able to generalize the above result and prove that if f _i and g _i are completely multiplicative, then we have where L _f(s) := _{n = 1} f(n)n ^–s is the Dirichlet series corresponding to f. Let r _N(n) be the number of solutions of x ₁ ² + ··· + x _N ² = n and r _2,P (n) be the number of solutions of x ² + Py ² = n. One of the applications of Theorem 2.1 is to obtain closed forms, in terms of (s) and Dirichlet L-functions, for the generating functions of r _N(n), r _N ²(n), r _2,P (n) and r _2,P (n)² for certain N and P. We also use these generating functions to obtain asymptotic estimates of the average values for each function for which we obtain a Dirichlet series.     

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.     

Cryptography in Quadratic Function Fields

We describe severalcryptographic schemes in quadratic function fields of odd characteristic.In both the real and the imaginary representation of such a field,we present a Diffie-Hellman-like key exchange protocol as wellas a public-key cryptosystem and a signature scheme of ElGamaltype. Several of these schemes are improvements of systems previouslyfound in the literature, while others are new. All systems arebased on an appropriate discrete logarithm problem. In the imaginarysetting, this is the discrete logarithm problem in the idealclass group of the field, or equivalently, in the Jacobian ofthe curve defining the function field. In the real case, theproblem in question is the task of computing distances in theset of reduced principal ideals, which is a monoid under a suitableoperation. Currently, the best general algorithms for solvingboth discrete logarithm problems are exponential (subexponentialonly in fields of high genus), resulting in a possibly higherlevel of security than that of conventional discrete logarithmbased schemes.     

Dirichlet Series Associated with Strongly q-Multiplicative Functions

In this work the Dirichlet series associated with real strongly q-multiplicative functions f(n) are studied. We will confine ourselves to the case _i=0 ^q–1 f(i) = 0. It is known that in this case the function _f (s) has an analytic continuation to the whole complex plane as an entire function with trivial zeros on the negative real line. The real function _f (t) satisfying the integral equation with delayed argument for some nonzero real _f naturally appears in the representation of the function _f (s). In this article we find some asymptotic properties of the function _f (s), prove that _f (s) is an entire function of order 2, and also prove that in the region the function _f (s) has only trivial zeros which are simple.     

Twisted higher moments of Kloosterman sums

Let be a nontrivial Dirichlet character modulo an odd prime . Write

We shall prove

and, for complex ,

0, \end{displaymath}">

where is a constant depending only on .

     

一类函数项级数的求和

以微分方程为工具 ,推出一类一致收敛且具有分析性质的函数项级数的求和公式 ,进而推广了五种基本幂级数 [1 ] 的和函数公式 .