English

Congruence Function Fields with Class Number One

Number Theory 2014-12-17 v1

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.

Keywords

Cite

@article{arxiv.1412.4824,
  title  = {Congruence Function Fields with Class Number One},
  author = {Martha Rzedowski-Calderón and Gabriel Villa-Salvador},
  journal= {arXiv preprint arXiv:1412.4824},
  year   = {2014}
}

Comments

8 pages

R2 v1 2026-06-22T07:32:41.227Z