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On the $2 k$ -th power mean of $\frac{L^{'}}{L} (1, χ)$ with the weight of Gauss sums

Dongmei Ren; Yuan Yi — 2009

Czechoslovak Mathematical Journal

The main purpose of this paper is to study the hybrid mean value of $\frac{L^{'}}{L} (1, χ)$ and Gauss sums by using the estimates for trigonometric sums as well as the analytic method. An asymptotic formula for the hybrid mean value $\sum_{χ \neq χ_{0}} | τ (χ) | | \frac{L^{'}}{L} {(1, χ) |}^{2 k}$ of $\frac{L^{'}}{L}$ and Gauss sums will be proved using analytic methods and estimates for trigonometric sums.

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