Browse > Article
http://dx.doi.org/10.4134/JKMS.2015.52.2.225

ON SUBFIELDS OF GK AND GENERALIZED GK FUNCTION FIELDS  

Danisman, Yusuf (Elementary Mathematics Education Mevlana University)
Ozdemir, Mehmet (Elementary Mathematics Education Mevlana University)
Publication Information
Journal of the Korean Mathematical Society / v.52, no.2, 2015 , pp. 225-237 More about this Journal
Abstract
In this article, we show that many of the genera that Giulietti and Fanali obtained from subfields of the GK curve can be obtained by using similar techniques used by Garcia, Stichtenoth and Xing. In the meantime, we obtain some new genera from the subfields of GK and generalized GK function fields.
Keywords
algebraic curves; function field; automorphism group;
Citations & Related Records
연도 인용수 순위
  • Reference
1 M. Abdon, J. Bezerra, and L. Quoos, Further examples of maximal curves, J. Pure Appl. Algebra 213 (2009), no. 6, 1192-1196.   DOI   ScienceOn
2 M. Abdon and L. Quoos, On the genera of subfields of the Hermitian function field, Finite Fields Appl. 10 (2004), no. 3, 271-284.   DOI   ScienceOn
3 I. Duursma and K.-H. Mak, On maximal curves which are not Galois subcovers of the Hermitian curve, Bull. Braz. Math. Soc. (N.S.) 43 (2012), no. 3, 453-465.   DOI   ScienceOn
4 S. Fanali and M. Giulietti, Quotient curves of the GK curve, Adv. Geom. 12 (2012), no. 2, 239-268.
5 A. Garcia, C. Guneri, and H. Stichtenoth, A generalization of the Giulietti-Korchmaros maximal curve, Adv. Geom. 10 (2010), no. 3, 427-434.   DOI
6 A. Garcia, H. Stichtenoth, and C.-P. Xing, On subfields of the Hermitian function field, Compositio Math. 120 (2000), no. 2, 137-170.   DOI   ScienceOn
7 M. Giulietti and G. Korchmaros, A new family of maximal curves over a finite field, Math. Ann. 343 (2009), no. 1, 229-245.   DOI
8 C. Guneri, M.Ozdemir, and H. Stichtenoth, The automorphism group of the generalized Giulietti-Korchmaros function field, Adv. Geom. 13 (2013), no. 2, 369-380.
9 G. Lachaud, Sommes d'Eisenstein et nombre de points de certaines courbes algebriques sur les corps finis, C. R. Acad. Sci. Paris Ser. I Math. 305 (1987), no. 16, 729-732.
10 H. G. Ruck and H. Stichtenoth, Characterization of Hermitian function fields over finite fields, J. Reine Angew. Math. 457 (1994), 185-188.
11 H. Stichtenoth, Uber die Automorphismengruppe eines algebraischen Funktionenkorpers von Primzahlcharakteristik. I, Arch. Math. 24 (1973), 527-544.   DOI
12 H. Stichtenoth, Uberber die Automorphismengruppe eines algebraischen Funktionenkorpers von Primzahlcharakteristik. II, Arch. Math. 24 (1973), 615-631.   DOI
13 H. Stichtenoth, Algebraic Function Fields and Codes, Springer-Verlag, Berlin, 2009.