대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제16권4호
  • /
  • Pages.595-606
  • /
  • 2001
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지

DETERMINATION OF CLASS NUMBERS OR THE SIMPLEST CUBIC FIELDS

  • 발행 : 2001.10.01
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초록

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.

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참고문헌

  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