Martha Rzedowski-Calderón, Gabriel Villa-Salvador
Published 2014-12-15Version 1
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.
Divisibility of class numbers of certain families of quadratic fields
Real cyclotomic fields of prime conductor and their class numbers
Lower bound for class number and a proof of Chowla and Yokoi's conjecture
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