Korean J. Math. Vol. 22 No. 3 (2014) pp.419-427
DOI: https://doi.org/10.11568/kjm.2014.22.3.419

Note on average of class numbers of cubic function fields

Article Sidebar

PDF
Published: Sep 30, 2014
Keywords:
Average of class numbers, cubic function field
Mathematics Subject Classification:
11R58, 11R16, 11R29

Main Article Content

Hwanyup Jung
Chungbuk national University

Abstract

Let $k=\mathbb{F}_q(T)$ be the rational function field over a finite field $\mathbb{F}_q$, 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 $k$.



Article Details

Supporting Agencies

This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education(2010-0008139).

References

[1] S. Bae, H. Jung, and P-L. Kang, Artin-Schreier extensions of the rational func- tion field, Math. Z. 276 (2014), 613–633. Google Scholar

[2] Y.-M. J. Chen, Average values of L-functions in characteristic two, J. Number Theory 128 (7) (2008), 2138–2158. Google Scholar

[3] J. Hoffstein and M. Rosen, Average values of L-series in function fields, J. Reine Angew. Math. 426 (1992), 117–150. Google Scholar

[4] C.-N. Hsu, On certain character sums over Fq[T], Proc. Amer. Math. Soc. 126 (3) (1998), 647–652. Google Scholar

[5] R. Prime, Averaging imaginary prime quadratic L-series, Preprint. Google Scholar

[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. Google Scholar