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 > 2 elements as its field of constants. We determine all such fields for which the class number is three. More precisely, we show that, up to Fq-isomorphism, there are only 8 of such function fields. For q = 2 the problem has been solved under the additional hypothesis that the function field is quadratic.
Lingua originaleEnglish
pagine (da-a)-
Numero di pagine10
RivistaDiscrete Mathematics
Volume312/3
Stato di pubblicazionePublished - 2012

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Algebraic Function Fields
Class number
Function Fields
Galois field
Isomorphism

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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