DOI QR코드

DOI QR Code

AVERAGE OF L-FUNCTIONS OF ARTIN-SCHREIER EXTENSIONS

  • Jung, Hwanyup (Department of Mathematics Education Chungbuk National University)
  • Received : 2016.07.17
  • Accepted : 2016.10.13
  • Published : 2016.11.15

Abstract

Let $k={\mathbb{F}}_q(t)$ be a rational function field over the finite field ${\mathbb{F}}_q$. In this paper we obtain formulas of average values of L-functions of some family of Artin-Schreier extensions over k.

Keywords

Acknowledgement

Supported by : Chungbuk National University

References

  1. S. Bae, H. Jung, and P-L. Kang Artin-Schreier extensions of the rational function field, Mathematische Zeitschrift 276 (2014), no. 3-4, 613-633. https://doi.org/10.1007/s00209-013-1215-0
  2. Y.-M. 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
  3. J. Hoffstein and M. Rosen, Average values of L-series in function fields, J. reine angew. Math. 426 (1992), 117-150.
  4. S. Hu and Y. Li, The genus fields of Artin-Schreier extensions, Finite Fields Appl. 16 (2010), no. 4, 255-264. https://doi.org/10.1016/j.ffa.2010.03.004
  5. R. Prime, Averaging imaginary prime quadratic L-series, Preprint.
  6. M. Rosen, Average value of class numbers in cyclic extensions of the rational function field, Number theory (Halifax, NS, 1994), 307-323, CMS Conf. Proc. 15 Amer. Math. Soc., Providence, RI, 1995.
  7. C. L. Siegel, The average measure of quadratic forms with given determinant and signature, Ann. Math. 45 (1944), 667-685. https://doi.org/10.2307/1969296
  8. L. A. Takhtadzhjan and A. I. Vinogradov, On analogues of the Gauss-Vinogradov formula. Soviet Math. Dokl. 22 (1980), 555-559.
  9. L. A. Takhtadzhjan and A. I. Vinogradov, Analogues of the Gauss-Vinogradov formula on the critical line, J. Soviet Math. 24 (1984), 183-208. https://doi.org/10.1007/BF01087241