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.
PICONE, A. (2012). On the Classification of Algebraic Function Fields of Class Number Three. DISCRETE MATHEMATICS, 312/3 [10.1016/j.disc.2011.05.014].
On the Classification of Algebraic Function Fields of Class Number Three
PICONE, Alberto
2012-01-01
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.
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