Mean values of derivatives of quadratic prime Dirichlet $L$-functions in function fields
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In this paper, we establish an asymptotic formula for mean value of $L^{(k)}(\frac{1}{2},\chi_{P})$ averaging over $\mb P_{2g+1}$ and over $\mb P_{2g+2}$ as $g\to\infty$ in odd characteristic. We also give an asymptotic formula for mean value of $L^{(k)}(\frac{1}{2},\chi_{u})$ averaging over $\mc I_{g+1}$ and over $\mc F_{g+1}$ as $g\to\infty$ in even characteristic.
Abstract
In this paper, we establish an asymptotic formula for mean value of $L^{(k)}(\frac{1}{2},\chi_{P})$ averaging over $\mb P_{2g+1}$ and over $\mb P_{2g+2}$ as $g\to\infty$ in odd characteristic. We also give an asymptotic formula for mean value of $L^{(k)}(\frac{1}{2},\chi_{u})$ averaging over $\mc I_{g+1}$ and over $\mc F_{g+1}$ as $g\to\infty$ in even characteristic.
참고문헌 (11)
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