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 analytic methods to study a limit problem involving the F Smarandache square complementary number Ssc（n）, and obtain its limit value.
The main purpose of this paper is using the elementary method to study a limit problem involving the F.Smarandache square complementary number, and obtain its limit value.
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
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
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.
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.
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
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Foundation item： Supported by the National Natural Science Foundation of China（10671055）
文摘The main purpose of this paper is using the analytic methods to study a limit problem involving the F Smarandache square complementary number Ssc（n）, and obtain its limit value.
文摘The main purpose of this paper is using the elementary method to study a limit problem involving the F.Smarandache square complementary number, and obtain its limit value.
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:
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 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.
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 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 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.
