Determination of all imaginary bicyclic biquadratic number fields of class number 3

  • Jung, Seok-Won (Department of Mathematics, Korea University, Seoul, 136-701) ;
  • Kwon, Soun-Hi (Department of Mathematics Education, Korea University, Seoul 136-701)
  • Published : 1998.02.01

Abstract

Using the list of all imaginary quadratic fields with class number 1, 2, 3 and 6, we determine all imaginary bicyclic biquadratic number fields of class number 3. There are exactly 163 such fields and their conductors are less than or equal to 163 $\cdot$883.

Keywords

References

  1. J. Reine Angew. Math. v.266 The imaginary bicyclic biquadratic fields with class number 1 E. Brown;C. J. Parry
  2. Math. Comp. v.31 On the imaginary bicyclic biquadratic fields with class number D. A. Buell;H. C.Williams;K. S.Williams,
  3. World Scientific Series in Pure Math. v.8 Class Number Parity P. E. Conner;J. Hurrelbrink
  4. Uber die Klassenzahl abelscher Zahlkorper H. Hasse
  5. J. Fac. Sci. Imp. Univ. Tokyo Sect. v.I 4 Uber den Dirichletschen KRorper S. Kuroda
  6. Acta Arith. v.LXVI. 3 Kuroda's class number formula F. Lemmermeyer
  7. Acta Arith. v.24 Notes on small class numbers H. L. Montgomery;P. J. Weinberger
  8. Math. Comp. v.35 The determination of all imaginary, quartic, abelian number fields with class number 1 B. Setzer
  9. Michigan Math. J. v.14 A complete determination of the comlex quadratic fields of class number one H. M. Stark
  10. Math. Comp. v.29 On complex quadratic fields with class number two H. M. Stark
  11. Math. Comp. v.65 Class number 5,6 and 7 C. Wagner
  12. Math. Comp. v.62 The determination of the imaginary abelian number fields with class number one K. Yamamura