In this paper,we use the elementary methods,the properties of Dirichlet character sums and the classical Gauss sums to study the estimation of the mean value of high-powers for a special character sum modulo a prime,a...In this paper,we use the elementary methods,the properties of Dirichlet character sums and the classical Gauss sums to study the estimation of the mean value of high-powers for a special character sum modulo a prime,and derive an exact computational formula.It can be conveniently programmed by the“Mathematica”software,by which we can get the exact results easily.展开更多
The main purpose of this paper is to use the mean value theorem of the Dirichlet L-function to study the distribution property of Dedekind sums, and to give a sharper mean value formula.
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 v...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.展开更多
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 val...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.展开更多
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.
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.
Let q 〉 4 be an integer. The main purpose of this paper is to study the mean value of Cochrane sum C（a, q） in quarter intervals, and obtain a sharp asymptotic formula for it.
Let n be any positive integer, and S（n） be the cubic complements of n. The main purpose of this paper is to study the asymptotic of ∑n≤x（n/S（n））^k （k ≥ 1）. And by using the elementary methods, it intends to...Let n be any positive integer, and S（n） be the cubic complements of n. The main purpose of this paper is to study the asymptotic of ∑n≤x（n/S（n））^k （k ≥ 1）. And by using the elementary methods, it intends to give two sharper asymptotic formulas, and thus extends the related conclusions.展开更多
The main purpose of this paper is using the properties of the classical Gauss sum and the analytic methods to study the computational problem of one kind of hybrid power mean involving the character sum of polynomials...The main purpose of this paper is using the properties of the classical Gauss sum and the analytic methods to study the computational problem of one kind of hybrid power mean involving the character sum of polynomials and a sum analogous to Kloosterman sum mod p,an odd prime,and give two sharp asymptotic formulae for them.展开更多
文摘In this paper,we use the elementary methods,the properties of Dirichlet character sums and the classical Gauss sums to study the estimation of the mean value of high-powers for a special character sum modulo a prime,and derive an exact computational formula.It can be conveniently programmed by the“Mathematica”software,by which we can get the exact results easily.
基金This work is supported by the National Natural Science Foundation of P. R. China
文摘The main purpose of this paper is to use the mean value theorem of the Dirichlet L-function to study the distribution property of Dedekind sums, and to give a sharper mean value formula.
基金Supported by National Natural Science Foundation of China （Grant No. 10671155） and Northwest University Innovation Fund （Grant No. 08YZZ30） The authors express their gratitude to the referee for his very helpful and detailed comments.
文摘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.
基金supported by National Natural Science Foundation of China (Grant No.10671155)
文摘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.
基金supported by National Natural Science Foundation of China (Grant No.11071194)
文摘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.
基金supported by National Natural Science Foundation of China(Grant Nos.11001218 and 11071194)the Research Fund for the Doctoral Program of Higher Education of China(Grant No.20106101120001)
文摘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.
基金supported by China Postdoctoral Science Foundation funded project (20080430202)the N.S.F.(10671155) of P.R.China
文摘Let q 〉 4 be an integer. The main purpose of this paper is to study the mean value of Cochrane sum C（a, q） in quarter intervals, and obtain a sharp asymptotic formula for it.
文摘Let n be any positive integer, and S（n） be the cubic complements of n. The main purpose of this paper is to study the asymptotic of ∑n≤x（n/S（n））^k （k ≥ 1）. And by using the elementary methods, it intends to give two sharper asymptotic formulas, and thus extends the related conclusions.
基金Supported by NSFC(No.12126357)Natural Science Basic Research Plan in Shaanxi Province of China(No.2023-JC-QN-0058)。
文摘The main purpose of this paper is using the properties of the classical Gauss sum and the analytic methods to study the computational problem of one kind of hybrid power mean involving the character sum of polynomials and a sum analogous to Kloosterman sum mod p,an odd prime,and give two sharp asymptotic formulae for them.
