Dedekind和的一些性质

木文用初等方法证明了Ｄｅｄｅｋｉｎｄ和的几个重要性质．主要结果是简化了Ｋｎｏｐｐ等式的证明并建立了一个类似的公式．运用同样的方法，还给出了Ｄｅｄｅｋｉｎｄ和互反律的另一个初等证明．     

一个类似于Dedekind和的均值公式

本文利用 Ｄｉｒｉｃｈｌｅｔ Ｌ－函数的均值定理以及 Ｄｅｄｅｋｉｎｄ和的性质研究一个类似于 Ｄｅｄｅｋｉｎｄ和的均值问题，并给出一个较精确的渐近公式．     

关于Dedekind和的均值公式

本文的主要目的是利用ＤｉｒｉｃｈｌｅｔＬ－函数的均值定理研究Ｄｅｄｅｋｉｎｄ和的值分布性质，并给出一个较强的均值公式．     

关于Dedekind和均值的渐近性质

本文的主要目的是利用Ｄｉｒｉｃｈｌｅｔ Ｌ－函数的均值定理研究Ｄｅｄｅｋｉｎｄ和的分布性质，并给出一个较强的渐近公式。     

关于高维Dedekind和的恒等式

以Ｄｏｎｚａｇｉｅｒ中高维Ｄｅｄｅｋｉｎｄ和为基础，研究了其算术性质，得到了一个有趣的恒等式。     

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．     

广义Dedekind和与L-函数的一类恒等式

本文的主要目的是引入广义 Ｄｅｄｅｋｉｎｄ和,并由此推出 Ｄｉｒｉｃｈｌｅｔ Ｌ－函数的 一类恒等式．     

On Right Hereditary Rings and Dedekind Domains

ＯｎＲｉｇｈｔＨｅｒｅｄｉｔａｒｙＲｉｎｇｓａｎｄＤｅｄｅｋｉｎｄＤｏｍａｉｎｓＬｉｕＺｈｏｎｇｋｕｉ（刘仲奎）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＮｏｒｔｈｗｅｓｔＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｌａｎｚｈｏｕ，７３００７０）Ａｂｓ...     

环的约化群与群环上的投射模

本文系统地研究群环的约化群，利用约化群刻划了群环上模的结构。主要结果：（１）Ｒ为交换半遗传环且Ｋ＿０Ｒ为挠群ｉｆｆ对任何有限生成半自反Ｒ－模Ｐ，ｓ＞０，使得．（２）设Ｒ为半局部Ｄｅｄｅｋｉｎｄ环，Ｇ为有限生成Ａｂｅｌ群，则Ｋ＿０ＲＧ为挠群ｉｆｆ如果Ｇ有素数ｐ阶元，则（３）如果Ｋ＿０ＲＧ为挠群，［Ｇ∶Ｈ］＜∞，则对任何，有．这里Ｒ为整环，Ｌ为其分式域。     

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。     

An interesting identity and asymptotic formula related to the Dedekind sums

We use the analytic methods and the properties of Gauss sums to study one kind mean value problems involving the classical Dedekind sums, and give an interesting identity and asymptotic formula for it.     

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．     

Values of zeta functions at negative integers, Dedekind sums and toric geometry

We study relations among special values of zeta functions, invariants of toric varieties, and generalized Dedekind sums. In particular, we use invariants arising in the Todd class of a toric variety to give a new explicit formula for the values of the zeta function of a real quadratic field at nonpositive integers. We also express these invariants in terms of the generalized Dedekind sums studied previously by several authors. The paper includes conceptual proofs of these relations and explicit computations of the various zeta values and Dedekind sums involved.

     

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.     

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.     

Dedekind zeta-functions and Dedekind sums

In this paper we use Dedekind zeta functions of two real quadratic number fields at -1 to denote Dedekind sums of high rank. Our formula is different from that of Siegel’s. As an application, we get a polynomial representation of ζK(-1): ζK(-1) = 1/45(26n³ -41n± 9),n = ±2(mod 5), where K = Q(√5q), prime q = 4n² + 1, and the class number of quadratic number field K2 = Q(vq) is 1.     

Dedekind和及第一类Chebyshev多项式

本文利用分析方法、Dedekind和及第一类Chebyshev多项式的算术性质,研究了一类关于Dedekind和及第一类Chebyshev多项式混合均值的渐近估计问题,并得到了一个较强的渐近公式.