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Keywords:
Dirichlet L-function; Gauss sums; asymptotic formula
Summary:
The main purpose of this paper is to study the hybrid mean value of $\frac {L'}L(1,\chi )$ and Gauss sums by using the estimates for trigonometric sums as well as the analytic method. An asymptotic formula for the hybrid mean value $\sum _{\chi \neq \chi _0} |\tau (\chi )| |\frac {L'}L(1,\chi )|^{2k}$ of $\frac {L'}L$ and Gauss sums will be proved using analytic methods and estimates for trigonometric sums.
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