A hybrid mean value involving two-term exponential sums and polynomial character sums |
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Authors: | Han Di |
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Affiliation: | 1. School of Mathematics, Northwest University, Xi’an, Shaanxi, P.R.China
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Abstract: | Let q ? 3 be a positive integer. For any integers m and n, the two-term exponential sum C(m, n, k; q) is defined by (C(m,n,k;q) = sumlimits_{a = 1}^q {e((ma^k + na)/q)} ) , where (e(y) = e^{2pi iy} ) . In this paper, we use the properties of Gauss sums and the estimate for Dirichlet character of polynomials to study the mean value problem involving two-term exponential sums and Dirichlet character of polynomials, and give an interesting asymptotic formula for it. |
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