带振荡系数的Kloosterman和

ａ，ｑ为正整数，且（ａ，ｑ）＝１，μ（ｎ）为Ｍｂｉｕｓ函数，带系数μ（ｎ）的不完整Ｋｌｏｏｓｔｅｒｍａｎ和定义为Ｓ（Ｎ，ａ，ｑ）＝∑ｎＮｎｎ≡１（ｍｏｄｑ）μ（ｎ）δｑ（ｎ）ｅａｎｑ，其中δｑ（ｎ）＝１如果（ｎ，ｑ）＝１，否则δｑ（ｎ）＝０本文建立如下较为精确的上界估计Ｓ（Ｎ，ａ，ｑ）Ｎｄ（ｑ）ｌｏｇ５２Ｎｑ１２＋ｑ１５ｌｏｇ１３５ＮＮ１５｛｝这个结果进一步改进了Ｈａｊｅｌａ，Ｐｏｌｉｎｇｔｏｎ以及Ｓｍｉｔｈ以前的工作     

积分算子的n-逼近数

本文研究了积分算子ＴＫ：Ｌｑ［０，１］→Ｌｑ［０，１］，（ｑ≥１）当核 Ｋ（ｓ， ｔ）是 Ｓｏｂｏｌｅｖ空间 Ｗｐｒ（［０， １］２）中元素时ｎ－逼近数 ａｎ（ＴＫ： Ｌｑ→ Ｌｑ）的估计，并把这个估计应用于退化核方法解第二类线性Ｆｒｅｄｈｏｌｍ方程（Ｉ一ＴＫ）ｘ＝ｙ时，Ｂａｄｈｖａｌｏｖ［５］意义下最佳误差的讨论中，所得到的最佳误差之估计当ｑ＝１时，最优化了［１０］的结论．     

A New Class of Generalized Landau Linear Positive Operator Sequence and Its Properties of Approximation

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＩｎ１９０８，Ｅ．Ｌａｎｄａｕｉｎｔｒｏｄｕｃｅｄｔｈｅｆｏｌｌｏｗｉｎｇｗｅｌｌｋｎｏｗｎｓｅｑｕｅｎｃｅｏｆｏｐｅｒａｔｏｒｓ［１］Ｌｎ［ｆ（ｔ）；ｘ］＝Ｋｎ∫１－１ｆ（ｔ）［１－（ｔ－ｘ）２］ｎｄｔ，　　　　（１．１）ｗｈｅｒｅ　　　　　Ｋｎ＝［∫１｛－１（１－ｔ２）ｎｄｔ］－１～ｎπ　　（ｎ→∞）．（１．１）ｗａｓｕｓｅｄｉｎｔｈｅｐｒｏｏｆｏｆｔｈｅＷｅｉｅｒｓｔｒａｓｓＴｈｅｏｒｅｍ．Ｓｉｎｃｅｔｈｅｎ，ｔｈｅａｐｐｒｏｘｉｍａｔｉｏｎｐｒｏｐ－ｅｒｔ…     

血生成模型的全局吸引性

在本文中，我们进一步研究时滞微分方程它由Ｍａｃｋｅｙ和Ｌａｄａｓ［２］提出作为血生成模型．我们建立了（＊）的平衡是全局吸引子的新的充分条件，我们还改进了Ｇｏｐａｌｓａｍｙ，Ｋｕｌｅｎｏｖｉｃ和Ｌａｄａｓ［１］所得到的某些结果．     

实二次函数域基本单位的范

作为Ｈ．Ｆ．Ｔｒｏｔｔｅｒ［３］中一个结果的模拟，本文给出实二次函数域Ｋ中基本单位ε的范为Ｎ（ε）＝ｇ的一些充分必要条件，其中ｇ为Ｋ的常数域Ｆｑ的非零乘法群Ｆｑ＾＊的生成元（２├ｑ）。利用图论的语言，本文还给出了Ｎ（ε）＝ｇ的一些充分条件，这些条件对于数域也同样地适用，从而推广了Ｔｒｏｔｔｅｒ［３］和前人工作中关于充分条件的结果。     

Quasi—uniformities on Lattice Implication Algebras

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｏｒｄｅｒｔｏｒｅｓｅａｒｃｈｔｈｅｌｏｇｉｃａｌｓｙｓｔｅｍｗｈｏｓｅｐｒｏｐｏｓｉｔｉｏｎａｌｖａｌｕｅｉｓｇｉｖｅｎｉｎａｌａｔｔｉｃｅ，ＸｕＹ．［Ｘｕ２］ｐｒｏｐｏｓｅｄｔｈｅｃｏｎｃｅｐｔｏｆｌａｔｔｉｃｅｉｍｐｌｉｃａｔｉｏｎａｌｇｅｂｒａａｎｄｄｉｓｃｕｓｓｅｄｉｔｓｓｏｍｅｐｒｏｐｅｒ－ｔｉｅｓｉｎ［Ｘｕ１］ａｎｄ［Ｘｕ２］．Ａｌｓｏ，ｉｎ［ＸＱ１］，ＸｕＹ．ｔｏｇｅｔｈｅｒｗｉｔｈＫ．Ｙ．Ｑｉｎｄｉｓｃｕｓｓｅｄｔｈｅｐｒｏｐ－ｅｒｔｉｅｓｏ…     

某些三维流形不变量的计算

Ｔｈｅｃａｌｃｕａｌｔｉｏｎｏｆ〈ｚｋ１,ｚｋ２,…,ｚｋｎ〉ＬｏｆｔｈｉｓｐａｐｅｒｗｉｌｌｂｅｉｎｔｅｒｍｏｆｔｈｅＫａｕｆｆｍａｎｂｒａｃｋｅｔ－ｐｏｌｙｎｏｍｉａｌ［１,２,３］．ＴｈｅＫａｕｆｆｍａｎｂｒａｃｋｅｔｐｏｌｙｎｏｍｉａｌｏｆａｐｌａｎａｒｄｉａｇｒａｍｏｆａｎｕｎｏｒｉｅｎｔｅｄｌｉｎｋｉｓａｎｅｌｅｍｅｎｔ〈Ｄ〉∈Ｚ［Ａ,Ａ－１］ｄｅｆｉｎｅｄｂｙｔｈｅｆｏｌｌｏｗｉｎｇｐｒｏｃｅｓｓ．ＡｓｔａｔｅｏｆＤｉｓｄｅｆｉｎｅｄｔｏｂｅａｍａｐｓｆｒｏｍｔｈｅｃｒｏｓｓｉｎｇ…     

解高维广义对称正则长波方程的Fourier谱方法

１引言对称正则长波方程（ＳＲＬＷＥ）是正则化长波方程（ＲＬＷＥ）的一种对称叙述［１］用于描述弱非线性作用下空间变换的离子声波传播．［１］得到了方程组（１．１）的双曲正割平方孤立波解、四个不变量和数值结果、明显地,从（１．１）中消去ρ,得到一类正则长波方程（ＲＬＷＥ）代替（１．２）中第三项、第四项对ｔ的导数为对ｘ的导数,得到Ｂｏｕｓｓｉｎｅｓｑ方程．［２］对一类广义对称正则长波方程组提出了谱方法,证明了古典光滑解的存在性和唯一性,建立了近似解的收敛性和误差估计。［３］研究了高维对称正则长波方程整体…     

Koch曲线的Hausdorff测度的估计

文［１］研究了Ｋｏｃｈ 曲线的Ｈａｕｓｄｏｒｆｆ测度,得到了一个改进了的上限,本文将进一步改进此上限． 有关的予备知识和结论可在［１］中见到．     

关于点可数覆盖

本文证明了（１）具有点可数基空间的商ｓ－像Ｘ有点可数基的充要条件是Ｘ是ｑ－空间；（２）度量空间的伪开ｓ－像若满足条件（＊），则它在伪开ｓ－映射下是保持的，（３）给出反例否定地回答了［１］和［２］中的问题．     

A Kuznetsov Formula for Kloosterman Sums on GLn

We prove a Kuznetsov sum formula for Kloosterman sums on GL _n corresponding to the big Bruhat cell. Using this formula, a weighted sum of Kloosterman sums can be expressed in spectral decomposition. A non-trivial estimate of the spectral side might lead to a proof of cancellations in sums of Kloosterman sums on GL _n.     

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.     

A generalization of power moments of Kloosterman sums

We find an expression for a sum which can be viewed as a generalization of power moments of Kloosterman sums studied by Kloosterman and Salié. Received: 24 March 2006     

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

The main purpose of this paper is using 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.     

On Z4-Linear Goethals Codes and Kloosterman Sums

Studying the coset weight distributions of the Z₄-linear Goethals codes, e connect these codes with the Kloosterman sums. From one side, e obtain for some cases, of the cosets of weight four, the exact expressions for the number of code ords of weight four in terms of the Kloosterman sums. From the other side, e obtain some limitations for the possible values of the Kloosterman sums, hich improve the well known results due to Lachaud and Wolfmann kn:lac.     

Elementary Proof of an Estimate for Kloosterman Sums with Primes

A new elementary proof of an estimate for incomplete Kloosterman sums modulo a prime q is obtained. Along with Bourgain’s 2005 estimate of the double Kloosterman sum of a special form, it leads to an elementary derivation of an estimate for Kloosterman sums with primes for the case in which the length of the sum is of order q^0.5+ε, where ε is an arbitrarily small fixed number.     

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.     

A transform property of Kloosterman sums

An expression for the number of times a certain trace function associated with a Kloosterman sum on an extension field assumes a given value in the base field is given and its properties explored. The relationship of this result to the enumeration of certain types of irreducible polynomials over fields of characteristic two or three and to the weights in the dual of a Melas code is considered. It is argued that the expressions obtained for the trace functions, while simply related to the Kloosterman sums, can be more directly useful than the exponential sums themselves in certain applications. In addition, they enjoy properties that are of independent interest.     

Kloosterman sum identities and low-weight codewords in a cyclic code with two zeros

We apply relations of n-dimensional Kloosterman sums to exponential sums over finite fields to count the number of low-weight codewords in a cyclic code with two zeros. As a corollary we obtain a new proof for a result of Carlitz which relates one- and two-dimensional Kloosterman sums. In addition, we count some power sums of Kloosterman sums over certain subfields.     

On Some Identities Involving Certain Hardy Sums and a Kloosterman Sum

Ukrainian Mathematical Journal - We propose a new reciprocity theorem for the Hardy sum s5(h, p). In addition, a hybrid mean-value problem involving the Hardy sum s4(h, p) and a Kloosterman sum is...