Edit Profile (opens in new tab) Louboutin, Stéphane R. Co-Author Distance Author ID: louboutin.stephane-r Published as: Louboutin, Stéphane; Louboutin, Stéphane R.; Louboutin, S.; Louboutin, S. R.; Louboutin, Stephane more...less Homepage: https://www.flickr.com/photos/139889408@N07 External Links: MGP · ORCID · Wikidata · Google Scholar · ResearchGate · Math-Net.Ru · dblp · IdRef · theses.fr Documents Indexed: 155 Publications since 1988 Co-Authors: 19 Co-Authors with 28 Joint Publications 346 Co-Co-Authors all top 5 Co-Authors 122 single-authored 7 Okazaki, Ryotaro 4 Mollin, Richard Anthony 4 Munsch, Marc 3 Boutteaux, Gérard 3 Kwon, Soun-Hi 2 Barrucand, Pierre-A. 2 Lefeuvre, Yann 2 Williams, Hugh Cowie 1 Ahn, Jeoung-Hwan 1 Barry, Amadou Diogo 1 Lemmermeyer, Franz Josef 1 Murchio, A. 1 Newman, Michael Frederick 1 Olivier, Michel 1 Park, Sun-Mi 1 Park, Youngho 1 Rivat, Joël 1 Sárközy, András 1 Yang, Hee-Sun all top 5 Serials 15 Journal of Number Theory 12 Acta Arithmetica 9 Comptes Rendus de l’Académie des Sciences. Série I 8 Colloquium Mathematicum 7 Mathematics of Computation 7 Proceedings of the American Mathematical Society 7 Publicationes Mathematicae Debrecen 6 Canadian Journal of Mathematics 6 Manuscripta Mathematica 4 Canadian Mathematical Bulletin 3 Nagoya Mathematical Journal 3 Proceedings of the Japan Academy. Series A 3 Bulletin of the Korean Mathematical Society 3 International Journal of Number Theory 2 Functiones et Approximatio. Commentarii Mathematici 2 Journal of the London Mathematical Society. Second Series 2 Journal of the Mathematical Society of Japan 2 Mathematische Nachrichten 2 Mathematica Slovaca 2 Transactions of the American Mathematical Society 2 Journal of the Ramanujan Mathematical Society 2 Tatra Mountains Mathematical Publications 2 Journal de Théorie des Nombres de Bordeaux 2 Acta Mathematica et Informatica Universitatis Ostraviensis 2 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 2 The Quarterly Journal of Mathematics 2 Moscow Mathematical Journal 1 Periodica Mathematica Hungarica 1 Bulletin of the London Mathematical Society 1 Czechoslovak Mathematical Journal 1 Journal für die Reine und Angewandte Mathematik 1 Japanese Journal of Mathematics. New Series 1 Mathematische Zeitschrift 1 Osaka Journal of Mathematics 1 Pacific Journal of Mathematics 1 Proceedings of the London Mathematical Society. Third Series 1 Tôhoku Mathematical Journal. Second Series 1 Acta Mathematica Hungarica 1 Journal of Symbolic Computation 1 Bulletin of the Polish Academy of Sciences, Mathematics 1 Experimental Mathematics 1 RIMS Kokyuroku 1 Journal of the Australian Mathematical Society 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris Fields 154 Number theory (11-XX) 2 Field theory and polynomials (12-XX) 1 Commutative algebra (13-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 130 Publications have been cited 715 times in 293 Documents Cited by ▼ Year ▼ Continued fractions and real quadratic fields. Zbl 0652.12002 Louboutin, Stéphane 24 1988 Determination of all non-normal quartic CM-fields and of all non-abelian normal octic CM-fields with class number one. Zbl 0809.11069 Louboutin, Stéphane; Okazaki, Ryotaro 24 1994 Explicit bounds for residues of Dedekind zeta functions, values of \(L\)-functions at \(s=1\), and relative class numbers. Zbl 0967.11049 Louboutin, Stéphane 20 2000 Explicit upper bounds for residues of Dedekind zeta functions and values of \(L\)-functions at \(s=1\), and explicit lower bounds for relative class numbers of CM-fields. Zbl 0998.11066 Louboutin, Stéphane 20 2001 Some exact formulas for mean values of Dirichlet \(L\)- functions. (Quelques formules exactes pour des moyennes de fonctions \(L\) de Dirichlet.) Zbl 0802.11032 Louboutin, Stéphane 20 1993 The class number one problem for some non-abelian normal CM-fields. Zbl 0893.11045 Louboutin, Stéphane; Okazaki, Ryotaro; Olivier, Michel 18 1997 Majorations explicites de \(|{}L(1, {\chi{}})|\). (Explicit upper bounds on \(|{}L(1, {\chi{}})|\)). Zbl 0774.11051 Louboutin, Stéphane 16 1993 The mean value of \(|L(k,\chi)|^2\) at positive rational integers \(k \geq 1\). Zbl 1013.11049 Louboutin, Stéphane 15 2001 Lower bounds for relative class numbers of CM-fields. Zbl 0795.11058 Louboutin, Stéphane 15 1994 Explicit lower bounds for residues at \(s=1\) of Dedekind zeta functions and relative class numbers of CM-fields. Zbl 1026.11085 Louboutin, Stéphane 15 2003 Upper bounds on \(| L(1,\chi)|\) and applications. Zbl 0912.11046 Louboutin, Stéphane 13 1998 The Brauer-Siegel theorem. Zbl 1078.11064 Louboutin, Stéphane R. 13 2005 On the divisibility of the class number of imaginary quadratic number fields. Zbl 1269.11111 Louboutin, Stéphane R. 13 2009 The class number one problem for some non-abelian normal CM-fields of 2-power degrees. Zbl 0891.11054 Louboutin, Stéphane; Okazaki, Ryotaro 12 1998 Determination of all nonquadratic imaginary cyclic number fields of 2- power degrees with ideal class groups of exponents \(\leq 2\). Zbl 0822.11072 Louboutin, Stéphane 11 1995 The class number one problem for some non-abelian normal CM-fields of degree 24. Zbl 1010.11063 Lemmermeyer, F.; Louboutin, S.; Okazaki, R. 11 1999 Lower bound for \(L(1,\chi)\) and determination of the principal totally imaginary sextic abelian fields. (Minoration au point 1 des fonctions \(L\) et détermination des corps sextiques abéliens totalement imaginaires principaux.) Zbl 0761.11041 Louboutin, Stéphane 11 1992 Class numbers of real quadratic fields, continued fractions, reduced ideals, prime-producing quadratic polynomials and quadratic residue covers. Zbl 0771.11039 Louboutin, S.; Mollin, R. A.; Williams, H. C. 11 1992 Determination of all quaternion octic CM-fields with class number 2. Zbl 0861.11064 Louboutin, Stéphane 11 1996 Explicit upper bounds of the residue at the point 1 of zeta functions of certain number fields. (Majorations explicites du résidu au point 1 des fonctions zêta de certains corps de nombres.) Zbl 1040.11081 Louboutin, Stéphane 10 1998 Computation of relative class numbers of imaginary abelian number fields. Zbl 0929.11065 Louboutin, Stéphane 9 1998 Groupe des classes d’idéaux triviaux. (Class group of trivial ideals). Zbl 0634.12008 Louboutin, Stéphane 8 1989 Computation of relative class numbers of CM-fields by using Hecke \(L\)-functions. Zbl 0931.11050 Louboutin, Stéphane 8 2000 Mean values of \(L\)-functions and relative class numbers of cyclotomic fields. Zbl 1240.11133 Louboutin, S. R. 8 2011 CM-fields with cyclic ideal class groups of 2-power orders. Zbl 0881.11078 Louboutin, Stéphane 8 1997 Explicit upper bounds of \(|L(1,\chi)|\). IV. (Majorations explicites de \(|L(1,\chi)|\). IV.) Zbl 0996.11051 Louboutin, Stéphane R. 8 2002 The fundamental unit of some quadratic, cubic or quartic orders. Zbl 1165.11076 Louboutin, Stéphane R. 8 2008 Minorations (sous l’hypothèse de Riemann généralisée) des nombres de classes des corps quadratique imaginaires. Application. (Explicit lower bounds for class numbers of imaginary quadratic fields (under the generalized Riemann hypothesis). Application). Zbl 0703.11048 Louboutin, Stéphane 8 1990 Explicit upper bounds for \(| L(1, \chi) |\). II. (Majorations explicites de \(| L(1, \chi) |\). II.) Zbl 0864.11042 Louboutin, Stephane 8 1996 The class number one problem for the non-abelian normal CM-fields of degree 16. Zbl 0881.11079 Louboutin, Stéphane 8 1997 A twisted quadratic moment for Dirichlet \(L\)-functions. Zbl 1314.11055 Louboutin, Stéphane R. 8 2014 On the numerical computation of the constants of the functional equations of \(L\)-functions associated to odd characters. (Sur le calcul numérique des constantes des équations fonctionnelles des fonctions \(L\) associées aux caractères impairs.) Zbl 0958.11063 Louboutin, Stéphane 7 1999 On the mean value of \(|L(1,\chi)|^2\) for odd primitive Dirichlet characters. Zbl 0947.11025 Louboutin, Stéphane 7 1999 Class-number problems for cubic number fields. Zbl 0826.11051 Louboutin, Stéphane 7 1995 On a problem of D. H. Lehmer. Zbl 1160.11039 Louboutin, Stéphane R.; Rivat, Joël; Sárközy, András 7 2007 Efficient computation of root numbers and class numbers of parametrized families of real abelian number fields. Zbl 1109.11065 Louboutin, Stéphane R. 7 2007 Computation of class numbers of number fields. (Calcul du nombre de classes des corps de nombres.) Zbl 0854.11060 Louboutin, Stéphane 7 1995 Non-{G}alois cubic number fields with exceptional units. Zbl 1399.11172 Louboutin, Stéphane R. 7 2017 Prime producing quadratic polynomials and class-numbers of real quadratic fields. Zbl 0711.11041 Louboutin, Stéphane 7 1990 \(L\)-functions and class numbers of imaginary quadratic fields and of quadratic extensions of an imaginary quadratic field. Zbl 0752.11046 Louboutin, Stéphane 7 1992 On the fundamental units of some cubic orders generated by units. Zbl 1307.11120 Lee, Jun Ho; Louboutin, Stéphane R. 7 2014 Computation of class numbers of quadratic number fields. Zbl 1030.11079 Louboutin, Stéphane 7 2002 Upper bounds for residues of Dedekind zeta functions and class numbers of cubic and quartic number fields. Zbl 1282.11150 Louboutin, Stéphane R. 6 2011 Explicit upper bounds on \(|L(1,\chi)|\). III. (Majorations explicites de \(|L(1,\chi)|\). III.) Zbl 0981.11031 Louboutin, Stéphane 6 2001 Computation of relative class numbers of CM-fields. Zbl 0879.11064 Louboutin, Stéphane 6 1997 Computation of relative class numbers of CM-fields: Application to octic quaternion CM-fields. (Calcul des nombres de classes relatifs: Application aux corps octiques quaternioniques à multiplication complexe.) Zbl 0795.11059 Louboutin, Stéphane 6 1993 On the class number one problem for non-normal quartic CM-fields. Zbl 0796.11050 Louboutin, Stéphane 6 1994 Twisted quadratic moments for Dirichlet \(L\)-functions. Zbl 1372.11090 Louboutin, Stéphane R. 6 2015 Some explicit upper bounds for residues of zeta functions of number fields taking into account the behavior of the prime \(2\). Zbl 1137.11072 Louboutin, Stéphane R. 5 2008 Hasse unit indices of dihedral octic CM-fields. Zbl 0972.11105 Louboutin, Stéphane 5 2000 On some cubic or quartic algebraic units. Zbl 1211.11121 Louboutin, Stéphane 5 2010 The class-number one problem for some real cubic number fields with negative discriminants. Zbl 1171.11057 Louboutin, Stéphane R. 5 2006 Computation of \(L(0,\chi)\) and of relative class numbers of CM-fields. Zbl 0985.11054 Louboutin, Stéphane 5 2001 The exponent three class group problem for some real cyclic cubic number fields. Zbl 0999.11068 Louboutin, Stéphane 5 2002 The class number one problem for the dihedral and dicyclic CM-fields. Zbl 1036.11056 Louboutin, Stéphane 5 1999 Explicit upper bounds for values at \(s=1\) of Dirichlet \(L\)-series associated with primitive even characters. Zbl 1044.11082 Louboutin, Stéphane R. 5 2004 Explicit upper bounds for \(| L(1,\chi)|\) for primitive characters \(\chi\). Zbl 1065.11063 Louboutin, Stéphane R. 5 2004 Lower bounds for relative class numbers of imaginary abelian number fields and CM-fields. Zbl 1122.11053 Louboutin, Stéphane R. 5 2006 Real zeros of Dedekind zeta functions. Zbl 1322.11118 Louboutin, Stéphane R. 5 2015 An explicit lower bound on moduli of Dirichlet \(L\)-functions at \(s = 1\). Zbl 1352.11078 Louboutin, Stéphane R. 5 2015 On the fundamental units of a totally real cubic order generated by a unit. Zbl 1283.11152 Louboutin, Stéphane R. 4 2012 Class number problems for dicyclic CM-fields. Zbl 0963.11065 Louboutin, S.; Park, Y.-H. 4 2000 Construction of the real dihedral number fields of degree \(2p\). Applications. Zbl 1128.11316 Louboutin, Stéphane; Park, Young-Ho; Lefeuvre, Yann 4 1999 Explicit upper bounds for \(|L(1,\chi)|\) for primitive even Dirichlet characters. Zbl 0997.11067 Louboutin, Stéphane 4 2002 Class number and class group problems for some non-normal totally real cubic number fields. Zbl 0997.11093 Louboutin, Stéphane 4 2001 The simplest quartic fields with ideal class groups of exponents less than or equal to 2. Zbl 1142.11365 Louboutin, Stéphane R. 4 2004 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). Zbl 0703.11050 Louboutin, Stéphane 4 1991 A finiteness theorem for imaginary abelian number fields. Zbl 0869.11089 Louboutin, Stéphane 4 1996 Computation of the relative class numbers of some Hilbert class fields. (Calcul des nombres de classes relatifs de certains corps de classes de Hilbert.) Zbl 0817.11049 Louboutin, Stéphane 4 1994 The class number one problem for the non-normal sextic CM-fields. II. Zbl 1042.11070 Boutteaux, Gérard; Louboutin, Stéphane 4 2002 The second and fourth moments of theta functions at their central point. Zbl 1308.11080 Louboutin, Stéphane R.; Munsch, Marc 4 2013 Class numbers of real cyclotomic fields. Zbl 1072.11081 Louboutin, Stéphane R. 3 2004 The nonquadratic imaginary cyclic fields of \(2\)-power degrees with class numbers equal to their genus class numbers. Zbl 0919.11071 Louboutin, Stéphane 3 1999 The imaginary cyclic sextic fields with class numbers equal to their genus class numbers. Zbl 0885.11057 Louboutin, Stéphane 3 1998 The non-normal quartic CM-fields and the dihedral octic CM-fields with ideal class groups of exponent \(\leq 2\). Zbl 1108.11085 Louboutin, Stéphane; Yang, Hee-Sun; Kwon, Soun-Hi 3 2004 Majoration au point 1 des fonctions L associées aux caractères de Dirichlet primitifs, ou au caractère d’une extension quadratique d’un corps quadratique imaginaire principal. (An upper bound for L(1,\(\chi\) ) where \(\chi\) is a primitive Dirichlet character or a character of a quadratic extension of a principal imaginary quadratic field). Zbl 0721.11049 Louboutin, Stéphane 3 1991 On the Frobenius-Rabinovich theorem. (Extensions du théorème de Frobenius-Rabinovitsch.) Zbl 0746.11044 Louboutin, Stéphane 3 1991 Resultants of cyclotomic polynomials. Zbl 0881.11073 Louboutin, S. 3 1997 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.) Zbl 0806.11048 Barrucand, Pierre; Louboutin, Stéphane 3 1993 Fundamental units for orders generated by a unit. Zbl 1414.11146 Louboutin, Stéphane R. 3 2015 Explicit upper bounds for residues of Dedekind zeta functions. Zbl 1410.11123 Louboutin, Stéphane R. 3 2015 Dedekind sums, mean square value of \(L\)-functions at \(s=1\) and upper bounds on relative class numbers. Zbl 1403.11070 Louboutin, Stéphane R. 3 2016 Discriminants of cyclic cubic orders. Zbl 1401.11142 Lee, Jun Ho; Louboutin, Stéphane R. 3 2016 The class number one problem for some non-normal sextic CM-fields. Zbl 1023.11057 Boutteaux, Gérard; Louboutin, Stéphane 3 2002 Resultants of Chebyshev polynomials: a short proof. Zbl 1368.11113 Louboutin, Stéphane R. 3 2013 On the size of \(L(1,\chi)\) and S. Chowla’s hypothesis implying that \(L(1,\chi)>0\) for \(s>0\) and for real characters \(\chi\). Zbl 1334.11069 Louboutin, S. 3 2013 Simple proofs of the Siegel-Tatuzawa and Brauer-Siegel theorems. Zbl 1114.11090 Louboutin, Stéphane R. 2 2007 The class number one problem for the dihedral CM-fields. Zbl 0958.11071 Lefeuvre, Yann; Louboutin, Stéphane 2 2000 Determination of all quaternion CM-fields with ideal class groups of exponent 2. Zbl 0952.11025 Louboutin, Stéphane; Okazaki, Ryotaro 2 1999 Quadratic fields with principal Hilbert class fields and with complex multiplication. (Corps quadratiques à corps de classes de Hilbert principaux et à multiplication complexe.) Zbl 0854.11058 Louboutin, Stéphane 2 1996 Upper bounds on \(L(1,\chi)\) taking into account a finite set of prime ideals. Zbl 1422.11230 Louboutin, Stéphane R. 2 2018 Efficient computation of class numbers of real Abelian number fields. Zbl 1067.11081 Louboutin, Stéphane R. 2 2002 On the use of explicit bounds on residues of Dedekind zeta functions taking into account the behavior of small primes. Zbl 1091.11039 Louboutin, Stéphane R. 2 2005 Numerical evaluation at negative integers of the Dedekind zeta functions of totally real cubic number fields. Zbl 1125.11352 Louboutin, Stéphane R. 2 2004 Powerful necessary conditions for class number problems. Zbl 0871.11078 Louboutin, Stéphane 2 1997 Determination of totally imaginary cyclic quartic fields with ideal class group of exponent \(\leq 2\). (Détermination des corps quartiques cycliques totalement imaginaires à groupe des classes d’idéaux d’exposant \(\leq 2\).) Zbl 0799.11046 Louboutin, Stéphane 2 1992 Corrections to: Some exact formulas for mean values of Dirichlet \(L\)-functions. (Corrections à: Quelques formules exactes pour des moyennes de fonctions \(L\) de Dirichlet.) Zbl 0802.11033 Louboutin, Stéphane 2 1994 The class number one problem for some non-normal CM-fields of degree \(2p\). Zbl 1275.11143 Ahn, Jeoung-Hwan; Boutteaux, Gérard; Kwon, Soun-Hi; Louboutin, Stéphane 2 2012 Exponents of the ideal class groups of CM number fields. Zbl 1049.11122 Louboutin, S.; Okazaki, R. 2 2003 Determination of the orders generated by a cyclic cubic unit that are Galois invariant. Zbl 1394.11073 Lee, Jun Ho; Louboutin, Stéphane R. 2 2015 Mean square values of \(L\)-functions over subgroups for nonprimitive characters, Dedekind sums and bounds on relative class numbers. Zbl 07756923 Louboutin, Stéphane R.; Munsch, Marc 1 2023 Second moment of Dirichlet \(L\)-functions, character sums over subgroups and upper bounds on relative class numbers. Zbl 1485.11128 Louboutin, Stéphane R.; Munsch, Marc 1 2021 On the continued fraction expansions of \(\sqrt{p}\) and \(\sqrt{2p}\) for primes \(p\equiv 3\pmod 4\). Zbl 1442.11015 Louboutin, Stéphane R. 2 2020 Non-Galois cubic number fields with exceptional units. II. Zbl 1453.11137 Louboutin, Stéphane R. 1 2020 On the discriminants of the powers of an algebraic integer. Zbl 1441.11270 Louboutin, Stéphane R. 1 2020 Representation of the elements of the finite field \(\mathbb{F}_p\) by fractions. Zbl 1449.11006 Louboutin, S.; Murchio, A. 2 2019 On the denominator of Dedekind sums. Zbl 1435.11076 Louboutin, Stéphane R. 1 2019 Twisted quadratic moments for Dirichlet \(L\)-functions at \(s = 2\). Zbl 1449.11086 Louboutin, Stéphane R. 1 2019 Upper bounds on \(L(1,\chi)\) taking into account a finite set of prime ideals. Zbl 1422.11230 Louboutin, Stéphane R. 2 2018 Non-{G}alois cubic number fields with exceptional units. Zbl 1399.11172 Louboutin, Stéphane R. 7 2017 Upper bounds on \(L(1,\chi)\) taking into account ramified prime ideals. Zbl 1428.11200 Louboutin, Stéphane R. 1 2017 Fundamental units for a family of totally real cubic orders and the Diophantine equation \(u(u+a)(u+2a)=v(v+1)\). Zbl 1375.11070 Louboutin, Stéphane R.; Lee, Jun Ho 1 2017 Dedekind sums, mean square value of \(L\)-functions at \(s=1\) and upper bounds on relative class numbers. Zbl 1403.11070 Louboutin, Stéphane R. 3 2016 Discriminants of cyclic cubic orders. Zbl 1401.11142 Lee, Jun Ho; Louboutin, Stéphane R. 3 2016 Discriminants of \(\mathfrak G n\)-orders. Zbl 1357.11113 Louboutin, Stéphane R. 1 2016 Twisted quadratic moments for Dirichlet \(L\)-functions. Zbl 1372.11090 Louboutin, Stéphane R. 6 2015 Real zeros of Dedekind zeta functions. Zbl 1322.11118 Louboutin, Stéphane R. 5 2015 An explicit lower bound on moduli of Dirichlet \(L\)-functions at \(s = 1\). Zbl 1352.11078 Louboutin, Stéphane R. 5 2015 Fundamental units for orders generated by a unit. Zbl 1414.11146 Louboutin, Stéphane R. 3 2015 Explicit upper bounds for residues of Dedekind zeta functions. Zbl 1410.11123 Louboutin, Stéphane R. 3 2015 Determination of the orders generated by a cyclic cubic unit that are Galois invariant. Zbl 1394.11073 Lee, Jun Ho; Louboutin, Stéphane R. 2 2015 A twisted quadratic moment for Dirichlet \(L\)-functions. Zbl 1314.11055 Louboutin, Stéphane R. 8 2014 On the fundamental units of some cubic orders generated by units. Zbl 1307.11120 Lee, Jun Ho; Louboutin, Stéphane R. 7 2014 Upper bounds on relative class numbers of cyclotomic fields. Zbl 1324.11063 Louboutin, S. 1 2014 The second and fourth moments of theta functions at their central point. Zbl 1308.11080 Louboutin, Stéphane R.; Munsch, Marc 4 2013 Resultants of Chebyshev polynomials: a short proof. Zbl 1368.11113 Louboutin, Stéphane R. 3 2013 On the size of \(L(1,\chi)\) and S. Chowla’s hypothesis implying that \(L(1,\chi)>0\) for \(s>0\) and for real characters \(\chi\). Zbl 1334.11069 Louboutin, S. 3 2013 On positive real zeros of theta and \(L\)-functions associated with real, even and primitive characters. Zbl 1299.11063 Louboutin, Stéphane R.; Munsch, Marc 2 2013 On the fundamental units of a totally real cubic order generated by a unit. Zbl 1283.11152 Louboutin, Stéphane R. 4 2012 The class number one problem for some non-normal CM-fields of degree \(2p\). Zbl 1275.11143 Ahn, Jeoung-Hwan; Boutteaux, Gérard; Kwon, Soun-Hi; Louboutin, Stéphane 2 2012 Mean values of \(L\)-functions and relative class numbers of cyclotomic fields. Zbl 1240.11133 Louboutin, S. R. 8 2011 Upper bounds for residues of Dedekind zeta functions and class numbers of cubic and quartic number fields. Zbl 1282.11150 Louboutin, Stéphane R. 6 2011 Some quartic number fields containing an imaginary quadratic subfield. Zbl 1250.11092 Louboutin, Stéphane R. 1 2011 On some cubic or quartic algebraic units. Zbl 1211.11121 Louboutin, Stéphane 5 2010 On the divisibility of the class number of imaginary quadratic number fields. Zbl 1269.11111 Louboutin, Stéphane R. 13 2009 On the fourth moment of theta functions at their central point. Zbl 1266.11089 Barry, Amadou Diogo; Louboutin, Stéphane R. 1 2009 Nonabelian normal CM-fields of degree \(2pq\). Zbl 1196.11151 Kwon, S.-H.; Louboutin, S.; Park, S.-M. 1 2009 The fundamental unit of some quadratic, cubic or quartic orders. Zbl 1165.11076 Louboutin, Stéphane R. 8 2008 Some explicit upper bounds for residues of zeta functions of number fields taking into account the behavior of the prime \(2\). Zbl 1137.11072 Louboutin, Stéphane R. 5 2008 On a problem of D. H. Lehmer. Zbl 1160.11039 Louboutin, Stéphane R.; Rivat, Joël; Sárközy, András 7 2007 Efficient computation of root numbers and class numbers of parametrized families of real abelian number fields. Zbl 1109.11065 Louboutin, Stéphane R. 7 2007 Simple proofs of the Siegel-Tatuzawa and Brauer-Siegel theorems. Zbl 1114.11090 Louboutin, Stéphane R. 2 2007 The class-number one problem for some real cubic number fields with negative discriminants. Zbl 1171.11057 Louboutin, Stéphane R. 5 2006 Lower bounds for relative class numbers of imaginary abelian number fields and CM-fields. Zbl 1122.11053 Louboutin, Stéphane R. 5 2006 The Brauer-Siegel theorem. Zbl 1078.11064 Louboutin, Stéphane R. 13 2005 On the use of explicit bounds on residues of Dedekind zeta functions taking into account the behavior of small primes. Zbl 1091.11039 Louboutin, Stéphane R. 2 2005 Explicit upper bounds for the residues at \(s=1\) of the Dedekind zeta functions of some totally real number fields. Zbl 1104.11051 Louboutin, Stéphane R. 1 2005 Explicit upper bounds for values at \(s=1\) of Dirichlet \(L\)-series associated with primitive even characters. Zbl 1044.11082 Louboutin, Stéphane R. 5 2004 Explicit upper bounds for \(| L(1,\chi)|\) for primitive characters \(\chi\). Zbl 1065.11063 Louboutin, Stéphane R. 5 2004 The simplest quartic fields with ideal class groups of exponents less than or equal to 2. Zbl 1142.11365 Louboutin, Stéphane R. 4 2004 Class numbers of real cyclotomic fields. Zbl 1072.11081 Louboutin, Stéphane R. 3 2004 The non-normal quartic CM-fields and the dihedral octic CM-fields with ideal class groups of exponent \(\leq 2\). Zbl 1108.11085 Louboutin, Stéphane; Yang, Hee-Sun; Kwon, Soun-Hi 3 2004 Numerical evaluation at negative integers of the Dedekind zeta functions of totally real cubic number fields. Zbl 1125.11352 Louboutin, Stéphane R. 2 2004 Remarks on S. Chowla’s hypothesis implying that \(L(s,\chi )>0\) for \(s>0\) and for real characters \(\chi\). Zbl 1112.11039 Louboutin, Stéphane R. 1 2004 Explicit lower bounds for residues at \(s=1\) of Dedekind zeta functions and relative class numbers of CM-fields. Zbl 1026.11085 Louboutin, Stéphane 15 2003 Exponents of the ideal class groups of CM number fields. Zbl 1049.11122 Louboutin, S.; Okazaki, R. 2 2003 Note on a hypothesis implying the non-vanishing of Dirichlet \(L\)-series \(L(s,\chi)\) for \(s>0\) and real characters \(\chi\). Zbl 1044.11081 Louboutin, Stéphane R. 1 2003 Explicit upper bounds of \(|L(1,\chi)|\). IV. (Majorations explicites de \(|L(1,\chi)|\). IV.) Zbl 0996.11051 Louboutin, Stéphane R. 8 2002 Computation of class numbers of quadratic number fields. Zbl 1030.11079 Louboutin, Stéphane 7 2002 The exponent three class group problem for some real cyclic cubic number fields. Zbl 0999.11068 Louboutin, Stéphane 5 2002 Explicit upper bounds for \(|L(1,\chi)|\) for primitive even Dirichlet characters. Zbl 0997.11067 Louboutin, Stéphane 4 2002 The class number one problem for the non-normal sextic CM-fields. II. Zbl 1042.11070 Boutteaux, Gérard; Louboutin, Stéphane 4 2002 The class number one problem for some non-normal sextic CM-fields. Zbl 1023.11057 Boutteaux, Gérard; Louboutin, Stéphane 3 2002 Efficient computation of class numbers of real Abelian number fields. Zbl 1067.11081 Louboutin, Stéphane R. 2 2002 Explicit upper bounds for residues of Dedekind zeta functions and values of \(L\)-functions at \(s=1\), and explicit lower bounds for relative class numbers of CM-fields. Zbl 0998.11066 Louboutin, Stéphane 20 2001 The mean value of \(|L(k,\chi)|^2\) at positive rational integers \(k \geq 1\). Zbl 1013.11049 Louboutin, Stéphane 15 2001 Explicit upper bounds on \(|L(1,\chi)|\). III. (Majorations explicites de \(|L(1,\chi)|\). III.) Zbl 0981.11031 Louboutin, Stéphane 6 2001 Computation of \(L(0,\chi)\) and of relative class numbers of CM-fields. Zbl 0985.11054 Louboutin, Stéphane 5 2001 Class number and class group problems for some non-normal totally real cubic number fields. Zbl 0997.11093 Louboutin, Stéphane 4 2001 Explicit bounds for residues of Dedekind zeta functions, values of \(L\)-functions at \(s=1\), and relative class numbers. Zbl 0967.11049 Louboutin, Stéphane 20 2000 Computation of relative class numbers of CM-fields by using Hecke \(L\)-functions. Zbl 0931.11050 Louboutin, Stéphane 8 2000 Hasse unit indices of dihedral octic CM-fields. Zbl 0972.11105 Louboutin, Stéphane 5 2000 Class number problems for dicyclic CM-fields. Zbl 0963.11065 Louboutin, S.; Park, Y.-H. 4 2000 The class number one problem for the dihedral CM-fields. Zbl 0958.11071 Lefeuvre, Yann; Louboutin, Stéphane 2 2000 Fast computation of relative class numbers of CM-fields. Zbl 1032.11047 Louboutin, Stéphane 1 2000 The class number one problem for some non-abelian normal CM-fields of degree 24. Zbl 1010.11063 Lemmermeyer, F.; Louboutin, S.; Okazaki, R. 11 1999 On the numerical computation of the constants of the functional equations of \(L\)-functions associated to odd characters. (Sur le calcul numérique des constantes des équations fonctionnelles des fonctions \(L\) associées aux caractères impairs.) Zbl 0958.11063 Louboutin, Stéphane 7 1999 On the mean value of \(|L(1,\chi)|^2\) for odd primitive Dirichlet characters. Zbl 0947.11025 Louboutin, Stéphane 7 1999 The class number one problem for the dihedral and dicyclic CM-fields. Zbl 1036.11056 Louboutin, Stéphane 5 1999 Construction of the real dihedral number fields of degree \(2p\). Applications. Zbl 1128.11316 Louboutin, Stéphane; Park, Young-Ho; Lefeuvre, Yann 4 1999 The nonquadratic imaginary cyclic fields of \(2\)-power degrees with class numbers equal to their genus class numbers. Zbl 0919.11071 Louboutin, Stéphane 3 1999 Determination of all quaternion CM-fields with ideal class groups of exponent 2. Zbl 0952.11025 Louboutin, Stéphane; Okazaki, Ryotaro 2 1999 Upper bounds on \(| L(1,\chi)|\) and applications. Zbl 0912.11046 Louboutin, Stéphane 13 1998 The class number one problem for some non-abelian normal CM-fields of 2-power degrees. Zbl 0891.11054 Louboutin, Stéphane; Okazaki, Ryotaro 12 1998 Explicit upper bounds of the residue at the point 1 of zeta functions of certain number fields. (Majorations explicites du résidu au point 1 des fonctions zêta de certains corps de nombres.) Zbl 1040.11081 Louboutin, Stéphane 10 1998 Computation of relative class numbers of imaginary abelian number fields. Zbl 0929.11065 Louboutin, Stéphane 9 1998 The imaginary cyclic sextic fields with class numbers equal to their genus class numbers. Zbl 0885.11057 Louboutin, Stéphane 3 1998 On the Diophantine equation \(xy+yz+zx=d\). Zbl 1024.11015 Louboutin, S.; Newman, M. F. 1 1998 The class number one problem for some non-abelian normal CM-fields. Zbl 0893.11045 Louboutin, Stéphane; Okazaki, Ryotaro; Olivier, Michel 18 1997 CM-fields with cyclic ideal class groups of 2-power orders. Zbl 0881.11078 Louboutin, Stéphane 8 1997 The class number one problem for the non-abelian normal CM-fields of degree 16. Zbl 0881.11079 Louboutin, Stéphane 8 1997 Computation of relative class numbers of CM-fields. Zbl 0879.11064 Louboutin, Stéphane 6 1997 Resultants of cyclotomic polynomials. Zbl 0881.11073 Louboutin, S. 3 1997 Powerful necessary conditions for class number problems. Zbl 0871.11078 Louboutin, Stéphane 2 1997 Determination of all imaginary abelian number fields with relative class numbers any \(2\)-power, which are composita of imaginary abelian number fields with prime power conductors. Zbl 0978.11061 Louboutin, Stéphane 1 1997 Class-group problems for cubic number fields. Zbl 0888.11044 Louboutin, Stéphane 1 1997 Determination of all quaternion octic CM-fields with class number 2. Zbl 0861.11064 Louboutin, Stéphane 11 1996 Explicit upper bounds for \(| L(1, \chi) |\). II. (Majorations explicites de \(| L(1, \chi) |\). II.) Zbl 0864.11042 Louboutin, Stephane 8 1996 A finiteness theorem for imaginary abelian number fields. Zbl 0869.11089 Louboutin, Stéphane 4 1996 Quadratic fields with principal Hilbert class fields and with complex multiplication. (Corps quadratiques à corps de classes de Hilbert principaux et à multiplication complexe.) Zbl 0854.11058 Louboutin, Stéphane 2 1996 ...and 30 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 302 Authors 59 Louboutin, Stéphane R. 15 Kwon, Soun-Hi 11 Mollin, Richard Anthony 5 Liu, Huaning 5 Munsch, Marc 4 Ahn, Jeoung-Hwan 4 Chakraborty, Kalyan 4 Chang, Ku-Young 4 Hoque, Azizul 4 Ichimura, Humio 4 Kawamoto, Fuminori 4 Lee, Ethan Simpson 4 Park, Sun-Mi 4 Togbé, Alain 4 Voight, John Michael 3 Azizi, Abdelmalek 3 Bayad, Abdelmejid 3 Chattopadhyay, Jaitra 3 Garcia, Stephan Ramon 3 Howe, Everett W. 3 Kishi, Yasuhiro 3 Lemmermeyer, Franz Josef 3 Linowitz, Benjamin 3 Okazaki, Ryotaro 3 Tomita, Koshi 3 Williams, Hugh Cowie 3 Yamamura, Ken 3 Yang, Hee-Sun 2 Amoroso, Francesco Antonio 2 Anand, Jaitra Chattopadhyay 2 Biró, András 2 Boutteaux, Gérard 2 Byeon, Dongho 2 Cho, Peter Jaehyun 2 Debaene, Korneel 2 Elma, Ertan 2 Giberson, Luke 2 Győry, Kálmán 2 Hamahata, Yoshinori 2 Hoshi, Akinari 2 James, Kevin 2 Kala, Vítězslav 2 Kanemitsu, Shigeru 2 Kim, Henry H. 2 Lee, Geon-No 2 Lee, Seok Hyeong 2 Lee, Seungjai 2 Lin, Xin 2 Ma, Rong 2 Mahapatra, Nimish Kumar 2 Murabayashi, Naoki 2 Özer, Özen 2 Pandey, Prem Prakash 2 Pollack, Paul 2 Ramaré, Olivier 2 Roy, Bidisha 2 Scholl, Travis 2 Srinivasan, Anitha 2 Streng, Marco 2 Trudgian, Tim 2 Trudgian, Timothy S. 2 Wang, Xiaohan 2 Zekhnini, Abdelkader 2 Zhang, Wenpeng 2 Zhang, Yulong 1 Adžaga, Nikola 1 Aistleitner, Christoph 1 Alkan, Emre 1 Amiri, Farahnaz 1 Aoki, Miho 1 Arul, Vishal 1 Aubry, Yves 1 Bajolet, Aurélien 1 Balady, Steve 1 Barbulescu, Razvan 1 Beers, J. 1 Beneish, Lea 1 Bengoechea, Paloma 1 Benmerieme, Y. 1 Bérczes, Attila 1 Bernard, Olivier 1 Bertók, Csanád 1 Bettin, Sandro 1 Biasse, Jean-François 1 Booker, Andrew R. 1 Bordellès, Olivier 1 Bordignon, Matteo 1 Bouhamza, Mostapha 1 Breuer, Thomas 1 Bröker, Reinier 1 Burns, David John 1 Bzdęga, Bartłomiej 1 Cai, Tianxin 1 Chandran, Arya 1 Chen, Mingjie 1 Chen, Zhixiong 1 Cheon, Seung Ju 1 Chidambaram, Shiva 1 Clark, Peter Louis 1 Cohen, Henri ...and 202 more Authors all top 5 Cited in 87 Serials 53 Journal of Number Theory 26 Mathematics of Computation 18 Proceedings of the Japan Academy. Series A 12 Journal de Théorie des Nombres de Bordeaux 11 International Journal of Number Theory 10 Proceedings of the American Mathematical Society 9 Acta Arithmetica 7 Archiv der Mathematik 7 The Ramanujan Journal 6 Functiones et Approximatio. Commentarii Mathematici 5 Manuscripta Mathematica 5 Nagoya Mathematical Journal 5 Transactions of the American Mathematical Society 4 Bulletin of the Australian Mathematical Society 4 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 4 Mathematische Zeitschrift 4 Bulletin of the Korean Mathematical Society 3 Annales de l’Institut Fourier 3 Czechoslovak Mathematical Journal 3 Journal of Algebra 2 Journal of Mathematical Analysis and Applications 2 Mathematical Proceedings of the Cambridge Philosophical Society 2 Canadian Mathematical Bulletin 2 Glasgow Mathematical Journal 2 Journal of Pure and Applied Algebra 2 Journal für die Reine und Angewandte Mathematik 2 Mathematica Slovaca 2 Mathematika 2 Acta Mathematica Hungarica 2 Expositiones Mathematicae 2 Chinese Science Bulletin 2 Acta Mathematica et Informatica Universitatis Ostraviensis 2 Acta Mathematica Sinica. English Series 2 Journal of the Australian Mathematical Society 2 Bulletin of the Brazilian Mathematical Society. New Series 2 Research in Number Theory 1 Rocky Mountain Journal of Mathematics 1 Mathematics Magazine 1 Acta Mathematica Vietnamica 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Applied Mathematics and Computation 1 Canadian Journal of Mathematics 1 Duke Mathematical Journal 1 Illinois Journal of Mathematics 1 International Journal of Mathematics and Mathematical Sciences 1 Inventiones Mathematicae 1 Journal of the London Mathematical Society. Second Series 1 Journal of the Mathematical Society of Japan 1 Mathematische Annalen 1 Mathematische Nachrichten 1 Osaka Journal of Mathematics 1 Pacific Journal of Mathematics 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Tôhoku Mathematical Journal. Second Series 1 Tokyo Journal of Mathematics 1 Bulletin of the Iranian Mathematical Society 1 Journal of the Ramanujan Mathematical Society 1 Japan Journal of Industrial and Applied Mathematics 1 Experimental Mathematics 1 Applied Mathematics. Series B (English Edition) 1 Filomat 1 Finite Fields and their Applications 1 Selecta Mathematica. New Series 1 Boletín de la Sociedad Matemática Mexicana. Third Series 1 Annals of Combinatorics 1 Journal of Integer Sequences 1 Annals of Mathematics. Second Series 1 LMS Journal of Computation and Mathematics 1 The Quarterly Journal of Mathematics 1 Moscow Mathematical Journal 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 JP Journal of Algebra, Number Theory and Applications 1 Mediterranean Journal of Mathematics 1 Sarajevo Journal of Mathematics 1 International Electronic Journal of Algebra (IEJA) 1 Journal of Mathematical Inequalities 1 Asian-European Journal of Mathematics 1 East Asian Mathematical Journal 1 Japanese Journal of Mathematics. 3rd Series 1 \(p\)-Adic Numbers, Ultrametric Analysis, and Applications 1 Annales Mathématiques du Québec 1 ISRN Combinatorics 1 Applied Mathematics and Nonlinear Sciences 1 Transactions of the American Mathematical Society. Series B 1 Journal of Siberian Federal University. Mathematics & Physics 1 AIMS Mathematics 1 Annales Henri Lebesgue all top 5 Cited in 18 Fields 288 Number theory (11-XX) 20 Algebraic geometry (14-XX) 6 Field theory and polynomials (12-XX) 5 Commutative algebra (13-XX) 5 Information and communication theory, circuits (94-XX) 3 Special functions (33-XX) 2 Combinatorics (05-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Associative rings and algebras (16-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 1 \(K\)-theory (19-XX) 1 Group theory and generalizations (20-XX) 1 Topological groups, Lie groups (22-XX) 1 Functions of a complex variable (30-XX) 1 Convex and discrete geometry (52-XX) 1 Differential geometry (53-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Computer science (68-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.