Acknowledgement
The second author was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (2020R1F1A1A01066105).
References
- J. Andrade, Mean values of derivatives of L-functions in function fields: II, J. Number Theory 183 (2018), 24-39. https://doi.org/10.1016/j.jnt.2017.08.038
- J. Andrade, Mean values of derivatives of L-functions in function fields: III, Proc. Roy. Soc. Edinburgh Sect. A 149 (2019), no. 4, 905-913. https://doi.org/10.1017/prm.2018.53
- J. Andrade and H. Jung, Mean values of derivatives of L-functions in function fields: IV, J. Korean Math. Soc. 58 (2021), no. 6, 1529-1547. https://doi.org/10.4134/JKMS.j210243
-
J. C. Andrade and J. P. Keating, The mean value of
$L(\frac{1}{2},X)$ in the hyperelliptic ensemble, J. Number Theory 132 (2012), no. 12, 2793-2816. https://doi.org/10.1016/j.jnt.2012.05.017 - J. Andrade and S. Rajagopal, Mean values of derivatives of L-functions in function fields: I, J. Math. Anal. Appl. 443 (2016), no. 1, 526-541. https://doi.org/10.1016/j.jmaa.2016.05.019
- S. Bae and H. Jung, Average values of L-functions in even characteristic, J. Number Theory 186 (2018), 269-303. https://doi.org/10.1016/j.jnt.2017.10.006
- Y.-M. J. Chen, Average values of L-functions in characteristic two, J. Number Theory 128 (2008), no. 7, 2138-2158. https://doi.org/10.1016/j.jnt.2007.12.011
- J. B. Conrey, The fourth moment of derivatives of the Riemann zeta-function, Quart. J. Math. Oxford Ser. (2) 39 (1988), no. 153, 21-36. https://doi.org/10.1093/qmath/39.1.21
- J. B. Conrey, M. O. Rubinstein, and N. C. Snaith, Moments of the derivative of characteristic polynomials with an application to the Riemann zeta function, Comm. Math. Phys. 267 (2006), no. 3, 611-629. https://doi.org/10.1007/s00220-006-0090-5
- S. M. Gonek, Mean values of the Riemann zeta function and its derivatives, Invent. Math. 75 (1984), no. 1, 123-141. https://doi.org/10.1007/BF01403094
- A. E. Ingham, Mean-value theorems in the theory of the Riemann zeta-function, Proc. London Math. Soc. (2) 27 (1927), no. 4, 273-300. https://doi.org/10.1112/plms/s2-27.1.273