The main purpose of this paper is using the analytic methods and the properties of the classical Gauss sums to study the computational problem of one kind hybrid power mean involving the character sums of polynomials and two-term exponential sums modulo , an odd prime, and give some sharp asymptotic formulas for them.
Key Words: Two-term exponential sums, character sums of polynomials,
hybrid power mean, analytic method, asymptotic formula.