Korean J. Math. Vol. 24 No. 4 (2016) pp.601-612
DOI: https://doi.org/10.11568/kjm.2016.24.4.601

Average of class numbers of some family of Artin-Schreier extensions of rational function fields

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Published: Dec 30, 2016
Keywords:
Class numbers, $L$-functions, Artin-Schreier extensions
Mathematics Subject Classification:
11R20, 11R29, 11R42, 11R58.

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Hwanyup Jung
Department of Mathematics Education Chungbuk National University Cheongju 361-763, Korea

Abstract

In this paper we obtain average of class numbers of some family of Artin-Schreier extensions of rational function field $\mathbb{F}_{q}(t)$, where $q$ is a power of $3$.


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References

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

[2] Y-M. Chen, Average values of L-functions in characteristic two, J. Number Theory 128 (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] S. Hu and Y. Li, The genus fields of Artin-Schreier extensions, Finite Fields Appl. 16 (2010), 255–264. Google Scholar

[5] H. Jung, Note on average of class numbers of cubic function fields, The Korean Journal of Mathematics 22 (2014), 419–427. Google Scholar

[6] H. Jung, Average of L-functions of some family of Artin-Schreier extensions over rational function fields, submitted. Google Scholar

[7] M. Rosen, Average value of class numbers in cyclic extensions of the rational function field, Number Theory.(Halifax, NS, 1994) (1995), 307-323. Google Scholar

[8] C. L. Siegel, The average measure of quadratic forms with given determinant and signature, Ann. of Math. (2) 45 (1944), 667–685. Google Scholar

[9] L. A. Takhtadzhyan and A. I. Vinogradov, Analogues of the Vinogradov-Gauss formula on the critical line, J. Soviet Math. 24 (1984), 183–208. Google Scholar