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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
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-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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【期刊论文】ON A COCHRANE SUM AND ITS HYBRID MEAN VALUE FORMULA (II)*
张文鹏, ZHANG WENPENG
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-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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【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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【期刊论文】ON THE GENERAL KLOOSTERMAN SUM AND ITS FOURTH POWER MEAN*
张文鹏, ZHANG WENPENG
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-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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【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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