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On a Problem of *** and General Kloosterman Sums

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Acta Mathematica Sinica,English Series 2004年第3期20卷 515-524页

作者： wenpengzhang ResearchCenterforBasicScience Xi'anJiaotongUniversityXi'an710072P.R.China

Let q ≥ 3 be an odd number, a be any fixed positive 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 (mod q). Let N(a, q) denote the number of all solutions of the congruent equation bc ≡ a (mod q) for 1 ≤ b, c < q in which b and c are of opposite parity, and let . 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 general Kloosterman sums.

关键词： A problem of D. H. Lehmer Error term Hybrid mean value formula

Some Identities Involving Certain Hardy Sums and Ramanujan Sum

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Acta Mathematica Sinica,English Series 2005年第1期21卷 109-116页

作者： HongYanLIU wenpengzhang DepartmentofMathematics NorthwestUniversityXi'an710069P.R.China DepartmentofMathematics NorthwestUniversityXi'an710069P.R.China//DepartmentofAppliedMathematicsXi'anUniversityofTechnologyXi'an710048P.R.China

The main purpose of this paper is, using the mean-value theorem of Dirichletl-functions, to study the distribution properties of the hybrid mean value involving certain Hardysums and Ramanujan sum, and give four inter... 详细信息

关键词： Certain Hardy sums Ramanujan sum Hybrid mean value Identities

An Application of Exponential Sum Estimates

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Acta Mathematica Sinica,English Series 2004年第5期20卷 851-858页

作者： YuanYI wenpengzhang ResearchCenterforBasicScience Xi'anJiaotongUniversityXi'an710049P.R.China

Let p be an odd prime and let δ be a fixed real number with 0<δ<*** an integer α with 0<α 详细信息

Let p be an odd prime and let δ be a fixed real number with 0<δ<*** an integer α with 0<α

关键词： Exponential sum Trigonometric sums Asymptotic formula

On the 2k-th Power Mean of Inversion of L-functions with the Weight of the Gauss Sum

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Acta Mathematica Sinica,English Series 2004年第1期20卷 175-180页

作者： YuanYI wenpengzhang ResearchCenterforBasicScience Xi'anJiaotongUniversityXi'an710067P.R.China ResearchCenterforBasicScience Xi'anJiaotongUniversityXi'an710067P.R.China

The main purpose of this paper is to use the estimate for character sums and the method of trigonometric sums to study the 2k-th power mean of the inversion of Dirichlet L-functions with the weight of the Gauss sums, ... 详细信息

关键词： Dirichlet L-functions Gauss sums Mean value Asymptotic formula