Congruence Function Fields with Class Number One
  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. 
Martha Rzedowski-Calder\'on and Gabriel Villa-Salvador
math.NT