Conformal mapping is an established tool in engineering that uses the analytic property of complex-variable functions to transform the boundary shape in boundary value problems of Laplace's equation in two dimensions.
The main purpose of this paper is using the analytic method and the properties of the character sums to study the hybrid mean value properties of G ( χ, n ; p ) and S ( χ, p ), and to give an interesting mean value formula.
The main purpose of this paper is using the analytic method and the properties of Kloosterman sums to study this problem, and prove the following result.
The main purpose of this paper is, using the analytic methods and the properties of Gauss sums, to study this problem and give a sharp upper bound estimate for (1.1).
The main purpose of this paper is using the analytic method and the properties of Gauss sums to study the 2k th power mean of G ( χ, m, n, c ; p ), and to give a sharp asymptotic formula for it.
The main purpose of this paper is, using the analytic methods and the properties of character sums, to study the computational problem of one kind of hybrid mean value involving the quadratic Gauss sums and a new sum analogous to Kloosterman sums, and to give an interesting hybrid mean value formula for it.
The main purpose of this paper is using the analytic methods and the properties of Gauss sums to study the computational problem of one kind of fourth power mean of two-term exponential sums, and to give an interesting identity and asymptotic formula for it.
The main purpose of this paper is using the analytic method and the properties of Kloosterman sums to study the estimate problem of the mean value ∑ a ∈ A χ ( a ), and give a sharp upper bound estimate for it, where χ denotes any non-principal even character mod p. MSC 11L40.
The main purpose of this paper is using the analytic methods and the properties of Gauss sums to study the computational problem of a new sum analogous to quadratic Gauss sums, and to give an interesting asymptotic formula for its 2k th power mean.
