Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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MEAN VALUES OF DERIVATIVES OF QUADRATIC PRIME DIRICHLET L-FUNCTIONS IN FUNCTION FIELDS

  • Jung, Hwanyup (Department of Mathematics Education Chungbuk National University)
  • Received : 2021.06.02
  • Accepted : 2021.10.07
  • Published : 2022.07.31
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Abstract

In this paper, we establish an asymptotic formula for mean value of $L^{(k)}({\frac{1}{2}},\;{\chi}_P)$ averaging over ℙ2g+1 and over ℙ2g+2 as g → ∞ in odd characteristic. We also give an asymptotic formula for mean value of $L^{(k)}({\frac{1}{2}},\;{\chi}_u)$ averaging over 𝓘g+1 and over 𝓕g+1 as g → ∞ in even characteristic.

Keywords

Acknowledgement

This work was conducted during the research year of Chungbuk National University in 2021.

References

  1. J. Andrade, S. Bae, and H. Jung, Average values of L-series for real characters in function fields, Res. Math. Sci. 3 (2016), Paper No. 38, 47 pp. https://doi.org/10.1186/s40687-016-0087-4
  2. J. Andrade and H. Jung, Mean values of derivatives of L-functions in function fields: IV, Submitted.
  3. 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
  4. 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
  5. S. Bae and H. Jung, Note on the mean values of derivatives of quadratic Dirichlet Lfunctions in function fields, Finite Fields Appl. 57 (2019), 249-267. https://doi.org/10.1016/j.ffa.2019.02.010
  6. S. Bae and H. Jung,Mean values of derivatives of L-functions in even characteristic, Submitted.
  7. A. Florea, Improving the error term in the mean value of L(${\frac{1}{2}}$, χ) in the hyperelliptic ensemble, Int. Math. Res. Not. IMRN 2017 (2017), no. 20, 6119-6148. https://doi.org/10.1093/imrn/rnv387
  8. A. Florea, The second and third moment of L(1/2, χ) in the hyperelliptic ensemble, Forum Math. 29 (2017), no. 4, 873-892. https://doi.org/10.1515/forum-2015-0152
  9. A. Florea, The fourth moment of quadratic Dirichlet L-functions over function fields, Geom. Funct. Anal. 27 (2017), no. 3, 541-595. https://doi.org/10.1007/s00039-017-0409-8
  10. M. Rosen, Number theory in function fields, Graduate Texts in Mathematics, 210, Springer-Verlag, New York, 2002. https://doi.org/10.1007/978-1-4757-6046-0
  11. Z. Rudnick, Traces of high powers of the Frobenius class in the hyperelliptic ensemble, Acta Arith. 143 (2010), no. 1, 81-99. https://doi.org/10.4064/aa143-1-5