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A hybrid mean value involving two-term exponential sums and polynomial character sums

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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 \(C(m,n,k;q) = \sum\limits_{a = 1}^q {e((ma^k + na)/q)} \), where \(e(y) = e^{2\pi iy} \). 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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Authors and Affiliations

  1. School of Mathematics, Northwest University, Xi’an, Shaanxi, P.R.China

    Han Di

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  1. Han Di
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Correspondence to Han Di.

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Di, H. A hybrid mean value involving two-term exponential sums and polynomial character sums. Czech Math J 64, 53–62 (2014). https://doi.org/10.1007/s10587-014-0082-0

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  • DOI: https://doi.org/10.1007/s10587-014-0082-0

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