Abstract
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 \( \sum\limits_{\chi \ne \chi _0 } {|\tau (\chi )||\frac{{L'}} {L}(1,\chi )|^{2k} } \) of \( \frac{{L'}} {L} \) and Gauss sums will be proved using analytic methods and estimates for trigonometric sums.
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