The main purpose of this paper is to use the estimate for character sums and the method of trigonometric sums to study the 2k-th power mean of the inversion of Dirichlet L-functions with the weight of the Gauss sums, ...The main purpose of this paper is to use the estimate for character sums and the method of trigonometric sums to study the 2k-th power mean of the inversion of Dirichlet L-functions with the weight of the Gauss sums, and give a sharper asymptotic formula.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
Let p be an odd prime and let δ be a fixed real number with 0<δ<2.For an integer α with 0<α<p,denote by ā the unique integer between 0 and p satisfying aā≡1(mod p).Further, let{x}denote the fraction...Let p be an odd prime and let δ be a fixed real number with 0<δ<2.For an integer α with 0<α<p,denote by ā the unique integer between 0 and p satisfying aā≡1(mod p).Further, let{x}denote the fractional part of x.We derive an asymptotic formula for the number of pairs of integers(a,b)with 1≤a≤p-1,1≤b≤p-1,|{a^k/p}+{b^k/p}-{(?)~l/p}-{(?)~l/p}|<δ.展开更多
The main purpose of this paper is to use estimates for character sums and analytic methods to study the first power mean of the inversion of Dirichlet L-functions with the weight of general quadratic Gauss sums,and th...The main purpose of this paper is to use estimates for character sums and analytic methods to study the first power mean of the inversion of Dirichlet L-functions with the weight of general quadratic Gauss sums,and three asymptotic formulae are obtained.展开更多
基金supported by the Doctorate Foundation of Xi'an Jiaotong University
文摘The main purpose of this paper is to use the estimate for character sums and the method of trigonometric sums to study the 2k-th power mean of the inversion of Dirichlet L-functions with the weight of the Gauss sums, and give a sharper asymptotic formula.
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.
文摘Let p be an odd prime and let δ be a fixed real number with 0<δ<2.For an integer α with 0<α<p,denote by ā the unique integer between 0 and p satisfying aā≡1(mod p).Further, let{x}denote the fractional part of x.We derive an asymptotic formula for the number of pairs of integers(a,b)with 1≤a≤p-1,1≤b≤p-1,|{a^k/p}+{b^k/p}-{(?)~l/p}-{(?)~l/p}|<δ.
文摘The main purpose of this paper is to use estimates for character sums and analytic methods to study the first power mean of the inversion of Dirichlet L-functions with the weight of general quadratic Gauss sums,and three asymptotic formulae are obtained.
