On the Classification of Algebraic Function Fields of Class Number Three

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Abstract

Let F be an algebraic function field of one variable having a finite field Fq with q > 2elements as its field of constants. We determine all such fields for which the class numberis three. More precisely, we show that, up to Fq-isomorphism, there are only 8 of suchfunction fields. For q = 2 the problem has been solved under the additional hypothesisthat the function field is quadratic.
Lingua originaleEnglish
Numero di pagine10
RivistaDiscrete Mathematics
Volume312/3
Stato di pubblicazionePublished - 2012

All Science Journal Classification (ASJC) codes

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  • ???subjectarea.asjc.2600.2607???

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