Geodesic
On the $2k$-th power mean of $\frac {L'}L(1,\chi )$ with the weight of Gauss sums
Czechoslovak Mathematical Journal, Tome 59 (2009) no. 3, pp. 781-789

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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.
Classification : 11L07, 11M20
Keywords: Dirichlet L-function; Gauss sums; asymptotic formula 
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     title = {On the $2k$-th power mean of $\frac {L'}L(1,\chi )$ with the weight of {Gauss} sums},
     journal = {Czechoslovak Mathematical Journal},
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Ren, Dongmei; Yi, Yuan. On the $2k$-th power mean of $\frac {L'}L(1,\chi )$ with the weight of Gauss sums. Czechoslovak Mathematical Journal, Tome 59 (2009) no. 3, pp. 781-789. http://geodesic.mathdoc.fr/item/CMJ_2009__59_3_a16/