Louboutin, Stéphane R. Upper bounds on residues of Dedekind zeta functions of non-normal totally real cubic fields. (English) Zbl 1470.11297 Acta Arith. 198, No. 3, 233-256 (2021). Reviewer: Władysław Narkiewicz (Wrocław) MSC: 11R42 11M20 11R11 11R16 PDFBibTeX XMLCite \textit{S. R. Louboutin}, Acta Arith. 198, No. 3, 233--256 (2021; Zbl 1470.11297) Full Text: DOI
Louboutin, Stéphane R. When is the order generated by a cubic, quartic or quintic algebraic unit Galois invariant: three conjectures. (English) Zbl 1524.11201 Czech. Math. J. 70, No. 4, 905-919 (2020). Reviewer: Claude Levesque (Québec) MSC: 11R27 11R16 11R20 PDFBibTeX XMLCite \textit{S. R. Louboutin}, Czech. Math. J. 70, No. 4, 905--919 (2020; Zbl 1524.11201) Full Text: DOI
Louboutin, Stéphane R. Non-Galois cubic number fields with exceptional units. II. (English) Zbl 1453.11137 J. Number Theory 206, 62-80 (2020). MSC: 11R16 11R27 PDFBibTeX XMLCite \textit{S. R. Louboutin}, J. Number Theory 206, 62--80 (2020; Zbl 1453.11137) Full Text: DOI
Louboutin, Stéphane R. Non-{G}alois cubic number fields with exceptional units. (English) Zbl 1399.11172 Publ. Math. Debr. 91, No. 1-2, 153-170 (2017). Reviewer: Władysław Narkiewicz (Wrocław) MSC: 11R16 11R27 PDFBibTeX XMLCite \textit{S. R. Louboutin}, Publ. Math. Debr. 91, No. 1--2, 153--170 (2017; Zbl 1399.11172) Full Text: DOI
Louboutin, Stéphane R. Upper bounds for residues of Dedekind zeta functions and class numbers of cubic and quartic number fields. (English) Zbl 1282.11150 Math. Comput. 80, No. 275, 1813-1822 (2011). Reviewer: Lejla Smajlovic (Sarajevo) MSC: 11R42 11R16 11R29 PDFBibTeX XMLCite \textit{S. R. Louboutin}, Math. Comput. 80, No. 275, 1813--1822 (2011; Zbl 1282.11150) Full Text: DOI
Louboutin, Stéphane R. Some quartic number fields containing an imaginary quadratic subfield. (English) Zbl 1250.11092 Colloq. Math. 122, No. 1, 139-148 (2011). Reviewer: Abdelmalek Azizi (Oujda) MSC: 11R16 11R27 11R29 11R09 PDFBibTeX XMLCite \textit{S. R. Louboutin}, Colloq. Math. 122, No. 1, 139--148 (2011; Zbl 1250.11092) Full Text: DOI Link
Louboutin, Stéphane R. Efficient computation of root numbers and class numbers of parametrized families of real abelian number fields. (English) Zbl 1109.11065 Math. Comput. 76, No. 257, 455-473 (2007). Reviewer: Abdelmalek Azizi (Oujda) MSC: 11Y40 11R16 11R20 11R29 11R42 PDFBibTeX XMLCite \textit{S. R. Louboutin}, Math. Comput. 76, No. 257, 455--473 (2007; Zbl 1109.11065) Full Text: DOI
Louboutin, Stéphane R. The class-number one problem for some real cubic number fields with negative discriminants. (English) Zbl 1171.11057 J. Number Theory 121, No. 1, 30-39 (2006). MSC: 11R16 11R29 11R42 PDFBibTeX XMLCite \textit{S. R. Louboutin}, J. Number Theory 121, No. 1, 30--39 (2006; Zbl 1171.11057) Full Text: DOI
Louboutin, Stéphane R. On the use of explicit bounds on residues of Dedekind zeta functions taking into account the behavior of small primes. (English) Zbl 1091.11039 J. Théor. Nombres Bordx. 17, No. 2, 559-573 (2005). Reviewer: Tauno Metsänkylä (Turku) MSC: 11R29 11R16 11R18 11R42 PDFBibTeX XMLCite \textit{S. R. Louboutin}, J. Théor. Nombres Bordx. 17, No. 2, 559--573 (2005; Zbl 1091.11039) Full Text: DOI Numdam Numdam EuDML
Louboutin, Stéphane R. The Brauer-Siegel theorem. (English) Zbl 1078.11064 J. Lond. Math. Soc., II. Ser. 72, No. 1, 40-52 (2005). Reviewer: Florin Nicolae (Berlin) MSC: 11R42 11R29 11R16 PDFBibTeX XMLCite \textit{S. R. Louboutin}, J. Lond. Math. Soc., II. Ser. 72, No. 1, 40--52 (2005; Zbl 1078.11064) Full Text: DOI
Louboutin, Stéphane R. The simplest quartic fields with ideal class groups of exponents less than or equal to 2. (English) Zbl 1142.11365 J. Math. Soc. Japan 56, No. 3, 717-727 (2004). MSC: 11R16 11R29 11R42 11Y40 PDFBibTeX XMLCite \textit{S. R. Louboutin}, J. Math. Soc. Japan 56, No. 3, 717--727 (2004; Zbl 1142.11365) Full Text: DOI
Louboutin, Stéphane The exponent three class group problem for some real cyclic cubic number fields. (English) Zbl 0999.11068 Proc. Am. Math. Soc. 130, No. 2, 353-361 (2002). Reviewer: Franz Lemmermeyer (San Marcos) MSC: 11R16 11R29 11R42 PDFBibTeX XMLCite \textit{S. Louboutin}, Proc. Am. Math. Soc. 130, No. 2, 353--361 (2002; Zbl 0999.11068) Full Text: DOI
Louboutin, Stéphane Class number and class group problems for some non-normal totally real cubic number fields. (English) Zbl 0997.11093 Manuscr. Math. 106, No. 4, 411-427 (2001). Reviewer: Franz Lemmermeyer (San Marcos) MSC: 11R29 11R16 11R42 PDFBibTeX XMLCite \textit{S. Louboutin}, Manuscr. Math. 106, No. 4, 411--427 (2001; Zbl 0997.11093) Full Text: DOI
Louboutin, Stéphane Computation of relative class numbers of imaginary cyclic fields of 2-power degrees. (English) Zbl 0902.11056 Buhler, J. P. (ed.), Algorithmic number theory. 3rd international symposium, ANTS-III, Portland, OR, USA, June 21–25, 1998. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 1423, 475-481 (1998). MSC: 11Y40 11R29 11R18 PDFBibTeX XMLCite \textit{S. Louboutin}, Lect. Notes Comput. Sci. 1423, 475--481 (1998; Zbl 0902.11056)
Louboutin, Stéphane Class-group problems for cubic number fields. (English) Zbl 0888.11044 Jap. J. Math., New Ser. 23, No. 2, 365-378 (1997). Reviewer: H.Yokoi (Iwasaki) MSC: 11R29 11R16 PDFBibTeX XMLCite \textit{S. Louboutin}, Jpn. J. Math., New Ser. 23, No. 2, 365--378 (1997; Zbl 0888.11044)
Louboutin, Stéphane Computation of class numbers of number fields. (Calcul du nombre de classes des corps de nombres.) (French) Zbl 0854.11060 Pac. J. Math. 171, No. 2, 455-467 (1995). Reviewer: S.Louboutin (Caen) MSC: 11R29 11Y40 11R42 PDFBibTeX XMLCite \textit{S. Louboutin}, Pac. J. Math. 171, No. 2, 455--467 (1995; Zbl 0854.11060) Full Text: DOI
Louboutin, Stéphane On the exponents of the ideal class groups of pure cubic fields. (Une remarque sur l’exposant du groupe des classes d’idéaux des corps cubiques.) (French) Zbl 0837.11060 C. R. Acad. Sci., Paris, Sér. I 320, No. 10, 1161-1163 (1995). Reviewer: C.Levesque (Quebec) MSC: 11R29 11R16 PDFBibTeX XMLCite \textit{S. Louboutin}, C. R. Acad. Sci., Paris, Sér. I 320, No. 10, 1161--1163 (1995; Zbl 0837.11060)
Louboutin, Stéphane Class-number problems for cubic number fields. (English) Zbl 0826.11051 Nagoya Math. J. 138, 199-208 (1995). Reviewer: S.Louboutin (Caen) MSC: 11R29 11R16 PDFBibTeX XMLCite \textit{S. Louboutin}, Nagoya Math. J. 138, 199--208 (1995; Zbl 0826.11051) Full Text: DOI
Louboutin, Stéphane The exponent 2-class-group problem for non-Galois over \(\mathbb{Q}\) quartic fields that are quadratic extensions of imaginary quadratic fields. (English) Zbl 0811.11066 J. Number Theory 49, No. 2, 133-141 (1994). Reviewer: K.S.Williams (Ottawa) MSC: 11R16 11R29 PDFBibTeX XMLCite \textit{S. Louboutin}, J. Number Theory 49, No. 2, 133--141 (1994; Zbl 0811.11066) Full Text: DOI
Louboutin, Stéphane; Okazaki, Ryotaro Determination of all non-normal quartic CM-fields and of all non-abelian normal octic CM-fields with class number one. (English) Zbl 0809.11069 Acta Arith. 67, No. 1, 47-62 (1994). Reviewer: S.Louboutin (Caen) MSC: 11R29 11R21 11R16 PDFBibTeX XMLCite \textit{S. Louboutin} and \textit{R. Okazaki}, Acta Arith. 67, No. 1, 47--62 (1994; Zbl 0809.11069) Full Text: DOI EuDML
Louboutin, Stéphane On the class number one problem for non-normal quartic CM-fields. (English) Zbl 0796.11050 Tôhoku Math. J., II. Ser. 46, No. 1, 1-12 (1994). Reviewer: S.Louboutin (Caen) MSC: 11R29 11R42 11R11 PDFBibTeX XMLCite \textit{S. Louboutin}, Tôhoku Math. J. (2) 46, No. 1, 1--12 (1994; Zbl 0796.11050) Full Text: DOI
Barrucand, Pierre; Louboutin, Stéphane Upper and lower bounds for the ideal class number of totally real fields of prime degree. (Majoration et minoration du nombre de classes d’idéaux des corps réels purs de degré premier.) (French) Zbl 0806.11048 Bull. Lond. Math. Soc. 25, No. 6, 533-540 (1993). Reviewer: K.S.Williams (Ottawa) MSC: 11R29 11R42 11R16 11R18 PDFBibTeX XMLCite \textit{P. Barrucand} and \textit{S. Louboutin}, Bull. Lond. Math. Soc. 25, No. 6, 533--540 (1993; Zbl 0806.11048) Full Text: DOI
Louboutin, Stéphane Determination of all imaginary cyclic quartic fields with ideal class groups of exponent \(\leqq 2\). (Détermination des corps quartiques cycliques totalement imaginaires à groupes des classes d’idéaux d’exposant \(\leqq 2\).) (French) Zbl 0782.11028 C. R. Acad. Sci., Paris, Sér. I 315, No. 3, 251-254 (1992). Reviewer: Richard A. Mollin (Calgary) MSC: 11R16 11R29 11R20 PDFBibTeX XMLCite \textit{S. Louboutin}, C. R. Acad. Sci., Paris, Sér. I 315, No. 3, 251--254 (1992; Zbl 0782.11028)
Louboutin, Stéphane \(L\)-functions and class numbers of imaginary quadratic fields and of quadratic extensions of an imaginary quadratic field. (English) Zbl 0752.11046 Math. Comput. 59, No. 199, 213-230 (1992). Reviewer: B.Z.Moroz (Bonn) MSC: 11R29 11R16 11R42 11R11 11-04 11Y40 PDFBibTeX XMLCite \textit{S. Louboutin}, Math. Comput. 59, No. 199, 213--230 (1992; Zbl 0752.11046) Full Text: DOI
Louboutin, Stéphane Norme relative de l’unité fondamentale et 2-rang du groupe des classes de certains corps biquadratiques. (Relative norm of the fundamental unit and 2-rank of the ideal class group of some biquadratic fields). (French) Zbl 0703.11050 Acta Arith. 58, No. 3, 273-288 (1991). Reviewer: S.Louboutin MSC: 11R16 11R29 11R27 PDFBibTeX XMLCite \textit{S. Louboutin}, Acta Arith. 58, No. 3, 273--288 (1991; Zbl 0703.11050) Full Text: DOI EuDML
Louboutin, Stéphane Quadratic extensions of the rational field, the Gauss field or the field of cubic roots of unity of caliber 1. (Les extensions quadratiques du corps des rationnels, ou du corps de Gauss, ou du corps des racines cubiques de l’unité de calibres 1.) (French) Zbl 0717.11047 Manuscr. Math. 69, No. 4, 387-410 (1990). Reviewer: Richard A. Mollin (Calgary) MSC: 11R29 11R11 11R16 PDFBibTeX XMLCite \textit{S. Louboutin}, Manuscr. Math. 69, No. 4, 387--410 (1990; Zbl 0717.11047) Full Text: DOI EuDML