Research of R. Okazaki

Papers

  1. Determination of Spaces of Hilber Cusp Forms,     Master Thesis, RIMS (1989).

  2. On evaluation of L-functions over real quadratic fields,  J. Math. Kyoto U. 31 (1991) 1125--1153.

  3. On an effective determination of a Shintani's decomposition of the cone R+n,    J. Math. Kyoto U. 33 (1993) 1057--1070.

  4. Determination of all non-normal quartic CM-fields and of all non-abelian normal octic CM-fields with class number one, Acta Arith. 67 (1994) 47--62, joint with S. Louboutin.

  5. Determination of all quaternion octic CM-fields with ideal class groups of exponent 2 (abridged version), Proc. Japan Acad. 70 (1994) 56--61, joint with S. Louboutin.

  6. An elementary proof for a Theorem of Thomas and Vasquez, J. Number Theory 55 (1995) 197--208.

  7. The class number one problem for some non-abelian normal CM-fields, Trans. A.M.S. 349 (1997) 3567--3678, joint with S. Louboutin and M. Olivier.

  8. The class number one problem for some non-abelian normal CM-fields of 2-power degrees, Proc. London Math. Soc. (3) 76 (1998) 523--548, joint with S. Louboutin.

  9. On a Shintani decomposition for a cubic field defined by X3+kX-1 = 0, in Number Theory --- Diophantine, computational and algebraic aspects, Proc. Int. Conf. Eger July 29--August 2, 1996, (ed. by K. Györy, A. Pehö and V. T. Sós),  from de Gruyter, Berlin...New York (1998) 445--451.

  10. The class number one problem for some non-abelian normal CM-fields of degree 24, J. Theor. Nombres Bordeaux 11 (1999) 387--406, joint with F. Lemmermeyer and S. Louboutin.

  11. Determination of all quaternion CM-fields with ideal class groups of exponent 2, Osaka J. Math. 36 (1999) 229--257,  joint with S. Louboutin.

  12. Non-normal class number one problem and the least prime power-residue, in Number Theory and its Applications, (ed. by K. Györy and S. Kanemitsu), from  Kluwer Academic publishers, (1999)  273--290.

  13. Inclusion of CM-fields and divisibility of relative class numbers, Acta Arith. 92 no. 4 (2000) 319--338.

  14. On Parities of Relative Class Numbers of Certain CM-Extensions, in Class Field Theory -- Its Centenary and Prospect, (ed. by K. Miyake), ASPM of Math. Soc. Japan 30 from Math. Soc. Japan (2001) 419--444.

  15. Geometry of a cubic Thue equation, Publ. Math. Debrecen 61 (2002) 267-314.
    [PDF-file]   [PS-file] ;     [text in DVI-file] ;     [figure in PDF-file]   [figure in PS-file]
  16. Exponents of the ideal class groups of CM number fields, Math. Z. 243 (2003) 155-159, joint with S. Louboutin.

Preprints

  1. Geometry of a quartic Thue equation.
    [text in PDF-file]   [text in PS-file]   [text in DVI-file]
  2. On class number one problem in non-normal sextic CM-fields.
    [PDF-file]   [PS-file]   [DVI-file]
  3. On class number one problem in non-normal sextic CM-fields with imaginary quadratic subfields.
    [PDF-file]   [PS-file]   [DVI-file]

Transparency

  1. Simplest cubic fields are non-isomorphic to each other.
    [text in PDF-file]   [text in PS-file]   [text in DVI-file]