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On Subfields of the Hermitian Function Field |
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| Authors: | Arnaldo Garcia Henning Stichtenoth Chao-Ping Xing |
| Institution: | (1) Instituto de Matématica Pura e Aplicada IMPA, 22460-320 Rio de Janeiro RJ, Brazil;(2) Mathematik u.Informatik, Universitäat GH Essen, FB 6, 45117 Essen, Germany;(3) Department of Mathematics, University of Scienceand Technology of China, Hefei, Anhui, 230026, P.R. China;(4) Department of InformationSystems and Computer Science, The National University of Singapore, 10Lower Kent Ridge, Crescent, Singapore, 119260 |
| Abstract: | The Hermitian function field H= K(x,y) is defined by the equationy
q+
y=x
q+1(q being a powerof the characteristic of K). OverK=
q
2 it is a maximalfunction field; i.e. the numberN(H)of
q2-rationalplaces attains the Hasse--Weil upper boundN(H)=q
2+1+2g(H)·q.All subfields K
EHare also maximal.In this paper we construct a large number of nonrational subfields EH, by considering the fixed fieldsH
under certaingroups
type="Italic">g 0 that occur as the genus of some maximal function field over
q
2. |
| Keywords: | function fields rational places finite fields |
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