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

1.1. 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. 130 (2002), 353-361.
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 $\le 2$. Math. Slovaca 54 (2004), 535-574.

1.2. 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), 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.
S. Louboutin and R. Okazaki. Exponents of the ideal class groups of CM number fields. Math. Z. 243 (2003), 155-159.

1.3. 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.

1.4. 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 $\vert L(k,\chi )\vert^2$ at positive rational integers $k\ge 1$. Colloquium Math. 90 (2001), 69-76.
S. Louboutin. Formulae for some Artin root numbers. Tatra Mountains Math. Publ. 20 (2000), 19-29.

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

3. List of publications list listAMS

4. 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.

CIRM2000
COLLOQUE " Algorithmes en théorie des nombres"
CIRM (Luminy, France), 15 - 19 mai 2000
Organisateur : F. Diaz y Diaz.

CIRM2002
RENCONTRE " Théorie des nombres et applications"
CIRM (Luminy, France), 14 - 18 Janvier 2002
Organisateurs : C. Mauduit, J. Rivat .

CIRM2003
ARITHMÉTIQUE, GÉOMÉTRIE ET THÉORIE DES CODES
CIRM (Luminy, France), 19 - 22 Mai 2003
Organisateurs : Gilles Lachaud, Yves Aubry, M. Tsfasman.

Quinzièmes rencontres arithmétiques de Caen :
Méthodes Analytiques en Théorie des Nombres, les 14, 15 et 16 Juin 2004.

ANTS6
Algorithmic Number Theory Symposium
University of Vermont, 13 - 18 June 2004.
CNTA8
Canadian Number Theory Association VIII Meeting, June 20-25, 2004, Toronto.

5. Links to Number Theory Webs:
Australia
USA

Hobbies
                             Climbing active volcanoes: Stromboli, Etna; Semeru, Krakatau, Merapi; Sakurajima; Ol Doinyo Lengai; Reventador, Tungurahua;..
                             To be climbed soon: Sangay
                             http://volcano.und.nodak.edu/
                             Mountaineering: Toubkal (4167m); Pic du Teide (3718m) (from the sea level); South Sister (3157m), Mt Adams (3742m), Mt Shasta (4317m);
                             Mt Fuji (3776m); Kilimanjaro (5895m); Aconcagua (6965m); Cotopaxi (5911m), Chimborazo (6310m), Tungurahua (5023m); ....
                             To be climbed soon: Mt Blanc, Mt Ararat

(Last update: December 6th (2004)).