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On the 2k-th power mean of \documentclass[12pt]{minimal}
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\frac{{L'}}
{L}(1,\chi )
$$\end{document} with the weight of Gauss sums
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Hybrid mean value of 2k\documentclass[12pt]{minimal}
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\begin{document}$$\varvec{2k}$$\end{document}-th power inversion of L\documentclass[12pt]{minimal}
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\begin{document}$$\varvec{L}$$\end{document}-functions and general quartic Gauss sums
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