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Mean values of derivatives of $L$-functions in even characteristic

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For any positive integer $\mu$, we compute the mean value of the $\mu$-th derivative of quadratic Dirichlet $L$-functions over the rational function field $\bF_{q}(t)$, where $q$ is a power of $2$.

Abstract

For any positive integer $\mu$, we compute the mean value of the $\mu$-th derivative of quadratic Dirichlet $L$-functions over the rational function field $\bF_{q}(t)$, where $q$ is a power of $2$.

참고문헌 (11)

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  2. J. Andrade, "Mean values of derivatives of L-functions in function fields : III", Proc. Roy. Soc. Edinburgh Sect. A, 149(4), pp.905~913 (2019)[DOI]
  3. Julio Andrade, "Mean values of derivatives of $L$-functions in function fields: IV", 대한수학회지, 58(6), pp.1529~1547 (2021), 대한수학회[DOI]
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  6. S. Bae, "Average values of L-functions in even characteristic", J. Number Theory, 186, pp.269~303 (2018)[DOI]
  7. Y. -M. J. Chen, "Average values of L-functions in characteristic two", J. Number Theory, 128(7), pp.2138~2158 (2008)[DOI]
  8. J. B. CONREY, "THE FOURTH MOMENT OF DERIVATIVES OF THE RIEMANN ZETA-FUNCTION", The Quarterly Journal of Mathematics, 39(1), pp.21~36 (1988), Oxford University Press (OUP)[DOI]
  9. J. B. Conrey, "Moments of the derivative of char"acteristic polynomials with an application to the Riemann zeta function", Comm. Math. Phys, 267(3), pp.611~629 (2006)[DOI]
  10. S. M. Gonek, "Mean values of the Riemann zeta function and its derivatives", Invent. Math, 75(1), pp.123~141 (1984)[DOI]
  11. A. E. Ingham, "Mean-Value Theorems in the Theory of the Riemann Zeta-Function", Proceedings of the London Mathematical Society, 27(4), pp.273~300 (1928), Wiley[DOI]

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