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
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 p and q be two distinct primes, epq（n） denotes the largest exponent of power pq which divides n. In this paper, we study the mean value properties of function epq（n）, and give some hybrid mean value formulas f...Let p and q be two distinct primes, epq（n） denotes the largest exponent of power pq which divides n. In this paper, we study the mean value properties of function epq（n）, and give some hybrid mean value formulas for epq（n） and Dirichlet divisor function d（n）. Key words： largest exponent; asymptotic formula; hybrid mean value; Dirichlet divisor function d（n）展开更多
The main purpose of this paper is using the analytic method to study the mean value properties of the arithmetical functions δk（（m, n））, δk（[m,n]/m）,and give several interesting asymptotic formulae for them.
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
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.
Ⅰ. INTRODUCTIONFor an integer q≥3, let X denote a typical Dirichlet character modulo q, and L(s, X) be the corresponding Dirichlet L-function. [1] studied the asymptotic property of mean value sum from X_q≠X_q^0 |L...Ⅰ. INTRODUCTIONFor an integer q≥3, let X denote a typical Dirichlet character modulo q, and L(s, X) be the corresponding Dirichlet L-function. [1] studied the asymptotic property of mean value sum from X_q≠X_q^0 |L(1, X)|~4, and showed the following asymptotic formula: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.
文摘Let p and q be two distinct primes, epq（n） denotes the largest exponent of power pq which divides n. In this paper, we study the mean value properties of function epq（n）, and give some hybrid mean value formulas for epq（n） and Dirichlet divisor function d（n）. Key words： largest exponent; asymptotic formula; hybrid mean value; Dirichlet divisor function d（n）
基金Supported by NSF of China(10671155)Supported by SF of Education Department of Shannxi Province(08JK291)
文摘The main purpose of this paper is using the analytic method to study the mean value properties of the arithmetical functions δk（（m, n））, δk（[m,n]/m）,and give several interesting asymptotic formulae for them.
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.
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.
文摘Ⅰ. INTRODUCTIONFor an integer q≥3, let X denote a typical Dirichlet character modulo q, and L(s, X) be the corresponding Dirichlet L-function. [1] studied the asymptotic property of mean value sum from X_q≠X_q^0 |L(1, X)|~4, and showed the following asymptotic formula:
