A Note on Class Numbers of the Simplest Cubic Fields

@article{Byeon1997ANO,
  title={A Note on Class Numbers of the Simplest Cubic Fields},
  author={Dongho Byeon},
  journal={Journal of Number Theory},
  year={1997},
  volume={65},
  pages={175-178}
}
  • Dongho Byeon
  • Published 1 July 1997
  • Mathematics
  • Journal of Number Theory
Abstract In this note, we extend the Uchida–Washington construction of the simplest cubic fields with class numbers divisible by a given rational integer, to the wildly ramified case, which was previously excluded. 
2 Citations
A NOTE ON CUBIC GALOIS EXTENSIONS
In this note we deal with the family of commutative cubic ring extensions Sk R, where k 2 R, Sk 1⁄4 R1⁄2X =ð fkÞ and fk 1⁄4 X 3 þ kX 2 ðkþ 3ÞXþ 1. For R being a field, every cubic Galois field

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Fundamental units in a family of cyclic cubic fields
For a family of cyclic cubic fields, we give a system of fundamental units, we obtain conditions sufficient to force the evenness of the classnumber hK, and we prove asymptotic results for the
Class numbers of the simplest cubic fields
Using the "simplest cubic fields" of D. Shanks, we give a modified proof and an extension of a result of Uchida, showing how to obtain cyclic cubic fields with class number divisible by n, for any n.
Class numbers of cubic cyclic fields
Let $n$ be any given positive integer. It is known that there exist real (imaginary) quadratic fields whose class numbers are divisible by $n$ . This is classical for imaginary case and the real case