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
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.
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.
On the mean value of Dedekind sum weighted by the quadratic Gauss sum
Various properties of classical Dedekind sums have been investigated by many authors. For example, Wenpeng Zhang, On the mean values of Dedekind sums, J. Théor. Nombres Bordx, 8 (1996), 429–442, studied the asymptotic behavior of the mean value of Dedekind sums, and H. Rademacher and E. Grosswald, Dedekind Sums, The Carus Mathematical Monographs No. 16, The Mathematical Association of America, Washington, D.C., 1972, studied the related properties. In this paper, we use the algebraic method to...
Some new sums related to D. H. Lehmer problem
About Lehmer’s number, many people have studied its various properties, and obtained a series of interesting results. In this paper, we consider a generalized Lehmer problem: Let be a prime, and let denote the number of all such that and . The main purpose of this paper is using the analytic method, the estimate for character sums and trigonometric sums to study the asymptotic properties of the counting function and give an interesting asymptotic formula for it.
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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