Korean Journal of Mathematics

  • 제22권3호
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  • Pages.419-427
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  • 2014
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  • 1976-8605(pISSN)
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  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
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NOTE ON AVERAGE OF CLASS NUMBERS OF CUBIC FUNCTION FIELDS

  • Jung, Hwanyup (Department of Mathematics Education Chungbuk National University)
  • 투고 : 2014.05.05
  • 심사 : 2014.07.25
  • 발행 : 2014.09.30
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초록

Let $k=\mathbb{F}_q(T)$ be the rational function field over a finite field $\mathbb{F}_q$, where $q{\equiv}1$ mod 3. In this paper, we determine asymptotic values of average of ideal class numbers of some family of cubic Kummer extensions of k.

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참고문헌

  1. S. Bae, H. Jung, and P-L. Kang, Artin-Schreier extensions of the rational function field, Math. Z. 276 (2014), 613-633. https://doi.org/10.1007/s00209-013-1215-0
  2. Y.-M. J. Chen, Average values of L-functions in characteristic two, J. Number Theory 128 (7) (2008), 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. C.-N. Hsu, On certain character sums over ${\mathbb{F}}_q[T]$, Proc. Amer. Math. Soc. 126 (3) (1998), 647-652. https://doi.org/10.1090/S0002-9939-98-04582-1
  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), CMS Conf. Proc., vol. 15, Amer. Math. Soc., Providence, RI, 1995, pp. 307-323.

피인용 문헌

  1. AVERAGE OF CLASS NUMBERS OF SOME FAMILY OF ARTIN-SCHREIER EXTENSIONS OF RATIONAL FUNCTION FIELDS vol.24, pp.4, 2014, https://doi.org/10.11568/kjm.2016.24.4.601