On the mean values of Dedekind sums
In this paper we study the asymptotic behavior of the mean value of Dedekind sums, and give a sharper asymptotic formula.
On the difference between a D. H. Lehmer number and its inverse modulo q
On the hybrid mean value of Dedekind sums and Hurwitz zeta-function
On the distribution of inverses modulo p (II)
A sum analogous to Dedekind sums and its hybrid mean value formula
Fourth power mean of character sums
A note on the Dirichlet characters of polynomials
A mean value related to the D. H. Lehmer problem and Kloosterman sums
On the Dirichlet characters of polynomials in several variables
On the Kummer conjecture
Hybrid mean value for a generalization of a problem of D. H. Lehmer
On the 2kth power mean of the character sums over short intervals
On the mean value of L(m,χ )L(n,χ̅) at positive integers m,n ≥ 1
Some applications of Bombieri's estimate for exponential sums
Some identities involving the Dirichlet L-function
An elliptic curve having large integral points
The main purpose of this paper is to prove that the elliptic curve has only the integral points and , using elementary number theory methods and some known results on quadratic and quartic Diophantine equations.
A hybrid mean value related to certain Hardy sums and Kloosterman sums
The main purpose of this paper is using the mean value formula of Dirichlet L-functions and the analytic methods to study a hybrid mean value problem related to certain Hardy sums and Kloosterman sums, and give some interesting mean value formulae and identities for it.
A hybrid mean value related to Dedekind sums
The main purpose of this paper is to study a hybrid mean value problem related to the Dedekind sums by using estimates of character sums and analytic methods.
On Lehmer's problem and Dedekind sums
Let be an odd prime and a fixed integer with . For each integer with , it is clear that there exists one and only one with such that (mod ). Let denote the number of all solutions of the congruence equation (mod ) for , in which and are of opposite parity, where is defined by the congruence equation . The main purpose of this paper is to use the properties of Dedekind sums and the mean value theorem for Dirichlet -functions to study the hybrid mean value problem involving...
Two identities related to Dirichlet character of polynomials
Let be a positive integer, denote any Dirichlet character . For any integer with , we define a sum analogous to high-dimensional Kloosterman sums as follows: where . The main purpose of this paper is to use elementary methods and properties of Gauss sums to study the computational problem of the absolute value , and give two interesting identities for it.
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