张文鹏
初等数论及解析数论的研究
个性化签名
- 姓名:张文鹏
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学术头衔:
博士生导师
- 职称:-
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学科领域:
数理逻辑与数学基础
- 研究兴趣:初等数论及解析数论的研究
张文鹏,男,陕西礼泉人,生于1958年8月。1979年9月考入陕西师范大学数学系学习,1983年6月考取山东大学数学系硕士研究生,师从于我国著名数学家潘承洞院士研究解析数论,1988年8月获理学博士学位后到西北大学数学系任教。1991年破格晋升为教授。现为西北大学数学系教授、博士生指导教师,西安交通大学基础科学研究中心教授、博士生指导教师,山东大学兼职教授、博士生指导教师,陕西师范大学、延安大学、渭南师范学院、咸阳师范学院兼职教授,兼任中国数学会理事、陕西省数学会副理事长及秘书长、《纯粹数学与应用数学》杂志副主编等职;被国家人事部选为“百千万”人才,评为陕西省有突出贡献专家,入选陕西省“三五”人才第一层。 在科研方面主要从事初等数论及解析数论的研究,先后承担国家自然科学基金项目、国家数学天元基金项目、国家“九五”数学重点项目、国家教委第四批重点跟踪支持人员基金项目、国家教委留学回国人员基金项目、中国博士后基金项目、陕西省自然科学基金项目、陕西省教委科研基金项目、陕西省“三五”人才专项奖金项目等二十多个科研项目的研究工作。目前共发表论文100余篇,SCI 共计61篇。
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4860
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成果阅读
439
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成果数
10
【期刊论文】ON THE GENERAL KLOOSTERMAN SUM AND ITS FOURTH POWER MEAN*
张文鹏, ZHANG WENPENG
,-0001,():
-1年11月30日
The main purpose of this paper is to study the asymptotic property of the fburth power mean of the general Kloostermaxl sums, and give an interesting calculating formula.
General Kloosterman sums, Fourth Dower mean, Asymptotic formula.,
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30浏览
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191下载
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【期刊论文】A PROBLEM OF D.H.LEHMER AND ITS MEAN SQUARE VALUE FORMULA*
张文鹏, ZHANG WENPENG, XU ZONGBEN AND YI YUAN
,-0001,():
-1年11月30日
Let q be an odd positive integer and let a be an integer coprime to q. For each integer b coprime to q with 1<b<q, there is a unique integer e coprimc to q with 1≤e≤q such that be≡a (rood q). Let N (a, q) denote the number of solutions of the congruence equation bc≡a (rood q) wlth 1≤b, c<q such that b,c are of opposite parity. The main purpose of this paper is using the properties of Dcdekind sums, the properties of Cochranc sums and the mean value theorem of Diriehlet L-thnetions to study the asymptotic property of the mean square value Σ(N(a,q)-2-1(q)2, and give a sharp asymptotic formula.
Lehmer Problem, Dedekind sums, Cochrane sum, Dirichlet L-function.,
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52浏览
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138下载
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【期刊论文】A NOTE ON THE COCHRANE SUM AND ITS HYBRID MEAN VALUE FORMULA*
张文鹏, ZHANG WENPENG AND LIU HUANING
,-0001,():
-1年11月30日
In this paper, we use the properties of Gauss sums, primitive characters and the mean value theorems of Dirlehlet L-functions to study the hybrid mean value of Cochrane suiils and general Kloosterman suins and give two sharp asymptotic formulac.
Cochrane sums, General Kloosterman sums, Asymptotic formula.,
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47浏览
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159下载
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【期刊论文】ON THE DIFFERENCE BETWEEN AN INTEGER AND ITS INVERSE MODULO N (II)*
张文鹏, ZHANG WENPENG
,-0001,():
-1年11月30日
The main purpose of this paper is using the mean value theorem of Dirichlet L-fhnetions to study the asymptotic property of one class number-theoretic ihnctions, and give an interesting mean square value formula.
An integer and its inverse, The error terms, Asymptotic formula.,
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45浏览
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143下载
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【期刊论文】SOME APPLICATIONS OF BOMBIERI'S ESTIMATE FOR EXPONENTIAL SUMS
张文鹏, ZHANG WENPENG AND YI YUAN
,-0001,():
-1年11月30日
Let p>3 bc a prime, k bc any fixed positlvc integer. For any polynomiM f(x, y) with rational integer coefficients, we define set A=A(f,k,δ)={(a,b):f(a,b)=O (modp), {ak-p}-{bk-p}<δ} whcrc 0<δ≤1, [x] denotes the grcatest intcger not exceeding x and {x}=x-[x]. The main purpose of this paper is to study the asymptotic behaviour of M(p,A,K)=Σpa=1 Σpb=1(a,b)4 and give an interesting asymptotic formula for M (p,A,k) for some special polynomials f (x, y).
Exponential sum, Bombieri', s estimates, Asymptotic formula.,
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51浏览
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184下载
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引用
【期刊论文】ON A PROBLEM OF D.H.LEHMER AND KLOOSTERMAN SUMS*
张文鹏, ZHANG WENPENG
,-0001,():
-1年11月30日
Let q≥3 is an odd number, a is any fixed positlvc integer with (a, q)=1. For each integer b with 1≤b<q and (b, q)=1, it is clear that there exists one and only one c with 0<c<q such that bc≡a (rood q). Lct N (a, q) denotcs thc numbcr of all solutions of the congruent equation bc≡a (mod q) for 1≤b, c<q in which b and c arc of opposite parity, and lct E(a, q)=N(a, q)-Ф(q). The main purpose of this paper is to study the distribution properties of E(a,q), and give a sharper hybrid mean value formula involving E (a, q) and Kloostcrman sums.
A problem of D., H., Lehmer, Error term, Hybrid mean value tbrmula.,
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40浏览
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106下载
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【期刊论文】ON A COCHRANE SUM AND ITS HYBRID MEAN VALUE FORMULA (II)*
张文鹏, ZHANG WENPENG
,-0001,():
-1年11月30日
The main purpose of this paper is using a mean value theorem of Dirieh-let L-ihnctions to study the asymptotic property of a hybrid mean value of a Coehrane sum, and givc an intercsting mean value formula.
A sum analogous to Dedckind sum, Mean value, Asymptotic formula.,
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33浏览
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118下载
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【期刊论文】ON DIRICHLET CHARACTERS OF POLYNOMIALS*
张文鹏, ZHANCI WENPENG AND YI YUAN
,-0001,():
-1年11月30日
The main purpose of this paper is using the properties of Gauss sums and aualytie method to study the calculating problem of one kind character sums modulo q, and give an interesting identity.
Dirichlct characters, Polynomials, Gauss sums, Analytic method.,
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40浏览
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120下载
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【期刊论文】MOMENTS OF GENERALIZED QUADRATIC GAUSS SUMS WEIGHTED BY L-FUNCTIONS*
张文鹏, ZHANG WENPENG
,-0001,():
-1年11月30日
The main purpose of this paper is using estimates tbr character sums and analytic methods to study the second, fourth, and sixth order moments of gcn-cralizcd quadratic Gauss sums weighted by L-thnctions. Three asymptotic tbrmulac arc obtalncd.
Gcncral quadratic Gauss sums, L-functions, Asymptotic formula.,
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46浏览
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95下载
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【期刊论文】ON THE DISTRIBUTION OF INVERSES MODULO P (II)
张文鹏, ZHANG WENPENG
,-0001,():
-1年11月30日
Let p bc an odd prime. For each integer a with 0<a<p, wc define by aa=1 rood p and 0<a<p. For any fixed positive integer k and any fixed real number 0<6<1, the main purpose of this paper is to study the distribution ehaviour of │p{ak-p}-p{-ka-p}│, and give a sharpcr asymptotic tbrmula.
General Kloostermann', s sums, Distribution of inverses modulo p.,
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55浏览
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105下载
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