Research

Algebraic Number Theory,
Zeta and L-functions of Number Fields,
Computational Number Theory.

Mathematics Subject Classification: 11M **, 11R** and 11Y**
Keywords: Class number, relative class number, CM-fields, Dedekind zeta functions , L-functions.

1. Latest Research Papers

General number fields:
S.Louboutin
         Class group problems for cubic number fields
          Japanese J. of Math. 23 (1997), 365-378.
S.Louboutin
         The exponent three class group problem for some real cyclic cubic number fields
          Proc. Amer. Math. Soc., to appear.

CM-fields
S. Louboutin
         CM-fields with cyclic ideal class groups of 2-power orders
          J. Number Theory 67 (1997), 1-10.
S. Louboutin, M. Olivier and R. Okazaki
         The class number one problem for some non-abelian normal CM-fields
          Trans. Amer. Math. Soc. 349 (1997), pp. 3657-3678.
S. Louboutin
         The class number one problem for the non-abelian normal CM-fields of degree 16
          Acta Arith. 82 (1997), 173-196.
S. Louboutin and R. Okazaki
         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.
S. Louboutin
         The class number one problem for the dihedral and dicyclic CM-fields
         Colloquium Math. 80 (1999), 259-265.

Imaginary abelian number fields
S. Louboutin
         The imaginary cyclic sextic fields with class numbers equal to their genus class numbers
          Colloquium Mathematicum 75 (1998), 205-212.
S. Louboutin
         The nonquadratic imaginary cyclic fields of 2-power degrees with class numbers equal to their genus class numbers
           Proc. Amer. Math. Soc. 127 (1999), 355-361.

Dedekind zeta functions and $L$-functions
S. Louboutin
          Majorations explicites du résidu au point 1 des fonctions zêta des corps de nombres
           J. Math. Soc. Japan 50 (1998), 57-69.
S. Louboutin
         Upper bounds on $\vert L(1,\chi )\vert$ and applications
          Canad. J. Math. 50 (1998), 794-815.
S. Louboutin
        On the mean value of $\vert L(1,\chi )\vert$ for odd primitive Dirichlet characters
         Proc. Japan Acad. 75 (1999), Ser. A, 143-145.
S. Louboutin
        Explicit bounds for residues of Dedekind zeta functions, values of $L$-functions at $s=1$, and relative class numbers
        J. Number Theory 85 (2000), 263-282.
S. Louboutin
       The mean value of $\vert L(k,\chi )\vert$ at positive rational integers $k\ge 1$
        Colloquium Math., to appear
S. Louboutin
        Formulae for some Artin root numbers.
       Tatra Mountains Math. Publ., to appear.

Algorithms and Numerical computations related to number fields
S. Louboutin
         Computation of relative class numbers of imaginary abelian number fields
          Exp. Math. 7 (1998), 293-303
S. Louboutin
        Sur le calcul numerique des constantes des equations fonctionnelles des fonctions $L$ associees aux caracteres impairs.
        (On the Artin root numbers of the $L$-functions associated with odd Dirichlet characters of prime conductors).
         C. R. Acad. Sci. Paris 329 (1999), 347-350.
S. Louboutin
        Computation of relative class numbers of CM-fields by using Hecke L-functions
         Math. Comp. 69 (2000), 371-393.
S. Louboutin
        Hasse unit indices of dihedral octic CM-fields
        Math. Nachr. 215 (2000), 107-113.
S. Louboutin
        Computation of $L(0,\chi )$ and of relative class numbers of CM-fields
        Nagoya Math. J. 161 (2001), 171-191.

2. Some Recent Preprints (copies will be provided on request)

S. Louboutin, H.-S. Yang and H.-S. Kwon

The non-normal quartic CM-fields and the dihedral octic CM-fields with ideal class groups of exponent $\le 2$

S. Louboutin and R. Okazaki

Exponents of the ideal class groups of the CM number fields

3. Abstracts of somme of these papers and preprints: Abstracts

Links

Conferences : Neuvièmes rencontres arithmétiques de Caen :
                        Méthodes Analytiques en Théorie des Nombres,
                        Les 29 et 30 Mai 1998.
                        The proceedings of this conference are available and will be provided under request.

                       Algebraic Number Theory and Diophantine Analysis,
                       ICM 1998 Satellite Conference, Graz,
                       August 31-September 4, 1998

Links to Number Theory Webs:
Australia
USA

Hobbies

(Last update: July 11th (2001)).