Congruence Function Fields with Class Number One

Abstract

We prove that there exists, up to isomorphism, exactly one function field over the finite field of two elements of class number one and genus four. This result, together with the ones of MacRae, Madan, Leitzel, Queen and Stirpe, establishes that there exist eight non-isomorphic congruence function fields of genus larger than zero and class number one.

8 pages