The main purpose of this paper is to use the analytic methods to study the hybrid mean value involving the hyper Cochrane sums, and give several sharp asymptotic formulae.
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 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...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 interesting identities.展开更多
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 ≡...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.展开更多
文摘The main purpose of this paper is to use the analytic methods to study the hybrid mean value involving the hyper Cochrane sums, and give several sharp asymptotic formulae.
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This work is supported by the NSF(10271093)the PNSF of P.R.China
文摘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 interesting identities.
文摘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.
