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Note on average of class numbers of cubic function fields
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Let k=bF_q(T) be the rational function field over a finite field bF_q, where q equiv 1 bmod 3. In this paper, we determine asymptotic values of average of ideal class numbers of some family of cubic Kummer extensions of k.
Abstract
Let k=bF_q(T) be the rational function field over a finite field bF_q, where q equiv 1 bmod 3. In this paper, we determine asymptotic values of average of ideal class numbers of some family of cubic Kummer extensions of k.
참고문헌 (6)
- S. Bae, "Artin-Schreier extensions of the rational function field", Math. Z, 276, pp.613~633 (2014)
- Y.-M. J. Chen, "Average values of L-functions in characteristic two", J. Number Theory, 128(7), pp.2138~2158 (2008)
- J. Hoffstein, "Average values of L-series in function fields", J. Reine Angew. Math, 426, pp.117~150 (1992)
- "Proc. Amer. Math. Soc", 1998, 647~652
- R. Prime, "Averaging imaginary prime quadratic L-series", Preprint, ~
- M. Rosen, "Average value of class numbers in cyclic extensions of the rational function field, Number theory (Halifax, NS, 1994)", CMS Conf. Proc., 15, pp.307~323 (1994), Amer. Math. Soc.
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