Function fields of class number one

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Sep 2015Embargo end date: 01 Jan 2014 English Publisher:Elsevier BVJournal:Journal of Number Theory, volume 154, pages 375-379 (issn: 0022-314X,

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Authors: Qibin Shen; Shuhui Shi;

doi: 10.1016/j.jnt.2015.02.005 , 10.48550/arxiv.1412.3505

arXiv: 1412.3505

Function fields of class number one

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Abstract

In 1975, [LMQ] listed 7 function felds over fnite felds (up to isomorphism) with positive genus and class number (i.e., the size of the divisor class group of degree zero) one and claimed to prove that these were the only ones such. In [S1], Claude Strirpe found 8th one! In this paper, we fix the argument in [LMQ] to show that this 8th example could have been found by [LMQ] method and is the only one, so that the list is now complete.

Related Organizations

University of Rochester
United States

Keywords

class number one, Arithmetic theory of algebraic function fields, Mathematics - Number Theory, FOS: Mathematics, Class numbers, class groups, discriminants, Number Theory (math.NT), congruence function fields

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