Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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DETERMINATION OF CLASS NUMBERS OR THE SIMPLEST CUBIC FIELDS

  • Published : 2001.10.01
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Abstract

Using p-adic class number formula, we derive a congru-ence relation for class numbers of the simplest cubic fields which can be considered as a cubic analogue of Ankeny-Artin-Chowlas theo-rem, Furthermore, we give an elementary proof for an upper bound for the class numbers of the simplest cubic fields.

Keywords

References

  1. Ann. of Math. v.56 The class number of real quadratic fields N.C. Ankeny;E. Artin;S. Chowla
  2. Primes of the form x²+ny² D.A. Cox
  3. Math. Comp. v.28 The simplest cubic fields D. Shanks
  4. Rational points on elliptic curves J.H. Silvermann;J. Tate
  5. Introduction to cyclotomic fields L.C. Washington
  6. Math. Comp. v.48 Class numbers of the simplest cubic fields