In this paper we prove that there are exactly eight function fields, up to isomorphism, over finite fields with class number one and positive genus. This classification was already suggested, although not completely proved, in a previous work about this topic.
Mercuri, P., Stirpe, C. (2015). Classification of algebraic function fields with class number one. JOURNAL OF NUMBER THEORY, 154, 365-374 [10.1016/j.jnt.2015.02.008].
Classification of algebraic function fields with class number one
MERCURI, PIETRO;
2015-09-01
Abstract
In this paper we prove that there are exactly eight function fields, up to isomorphism, over finite fields with class number one and positive genus. This classification was already suggested, although not completely proved, in a previous work about this topic.
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