Habsieger, Laurent 1963
Overview
Works:  22 works in 34 publications in 3 languages and 186 library holdings 

Roles:  Author, 956, Opponent, Thesis advisor, Editor 
Publication Timeline
.
Most widely held works by
Laurent Habsieger
Leçons de mathématiques d'aujourd'hui(
Book
)
1 edition published in 2003 in French and held by 82 WorldCat member libraries worldwide
1 edition published in 2003 in French and held by 82 WorldCat member libraries worldwide
Exercices corrigés de mathématiques (options M, P) posés à l'oral des concours ENSI(
Book
)
2 editions published in 1986 in French and held by 31 WorldCat member libraries worldwide
2 editions published in 1986 in French and held by 31 WorldCat member libraries worldwide
Conjectures de MacDonald et Qintegrale de SelbergAskey by
Laurent Habsieger(
Book
)
5 editions published in 1987 in French and held by 18 WorldCat member libraries worldwide
LA PRESENTE THESE REGROUPE LES DIFFERENTES CONTRIBUTIONS QU'A APPORTEES L'AUTEUR A L'ETUDE DES CONJECTURES DE MACDONALD. LE BUT DE L'INTRODUCTION EST DE DECRIRE L'ETAT ACTUEL DES CONNAISSANCES DANS CE DOMAINE ET DANS LES SUJETS S'Y RAPPORTANT. DANS LE CHAPITRE 2, LE QANALOGUE D'ASKEY DE L'INTEGRALE DE SELBERG EST PROUVE, AINSI QU'UNE CONJECTURE DE MORRIS. ON TROUVE DANS LE CHAPITRE 3 LA DEMONSTRATION DE LA CONJECTURE DE MACDONALD POUR LE SYSTEME DE RACINES G::(2). LE CHAPITRE 4 REPREND UN ARTICLE DE STEMBRIDGE, EN SIMPLIFIANT SA PREUVE PAR DES CHANGEMENT DE NOTATIONS, ET EN OPERANT QUELQUES GENERALISATIONS. LE CHAPITRE 5 DONNE UNE INTERPRETATION COMBINATOIRE, SIMPLE ET NATURELLE, D'UN ALGORITHME DE ZEILBERGER. ENFIN, LE CHAPITRE 6 PROPOSE UNE NOUVELLE APPROCHE DE LA CONJECTURE DE DYSON, QUI PERMET DE RETROUVER UN GRAND NOMBRE DE CAS PARTICULIERS CONNUS
5 editions published in 1987 in French and held by 18 WorldCat member libraries worldwide
LA PRESENTE THESE REGROUPE LES DIFFERENTES CONTRIBUTIONS QU'A APPORTEES L'AUTEUR A L'ETUDE DES CONJECTURES DE MACDONALD. LE BUT DE L'INTRODUCTION EST DE DECRIRE L'ETAT ACTUEL DES CONNAISSANCES DANS CE DOMAINE ET DANS LES SUJETS S'Y RAPPORTANT. DANS LE CHAPITRE 2, LE QANALOGUE D'ASKEY DE L'INTEGRALE DE SELBERG EST PROUVE, AINSI QU'UNE CONJECTURE DE MORRIS. ON TROUVE DANS LE CHAPITRE 3 LA DEMONSTRATION DE LA CONJECTURE DE MACDONALD POUR LE SYSTEME DE RACINES G::(2). LE CHAPITRE 4 REPREND UN ARTICLE DE STEMBRIDGE, EN SIMPLIFIANT SA PREUVE PAR DES CHANGEMENT DE NOTATIONS, ET EN OPERANT QUELQUES GENERALISATIONS. LE CHAPITRE 5 DONNE UNE INTERPRETATION COMBINATOIRE, SIMPLE ET NATURELLE, D'UN ALGORITHME DE ZEILBERGER. ENFIN, LE CHAPITRE 6 PROPOSE UNE NOUVELLE APPROCHE DE LA CONJECTURE DE DYSON, QUI PERMET DE RETROUVER UN GRAND NOMBRE DE CAS PARTICULIERS CONNUS
Analyse by
Laurent Habsieger(
Book
)
1 edition published in 1986 in French and held by 12 WorldCat member libraries worldwide
1 edition published in 1986 in French and held by 12 WorldCat member libraries worldwide
Good and bad radii of convex polygons by
Peter Gritzmann(
Book
)
4 editions published between 1989 and 1990 in English and German and held by 8 WorldCat member libraries worldwide
4 editions published between 1989 and 1990 in English and German and held by 8 WorldCat member libraries worldwide
Une Qintegrale de SelbergAskey by
Laurent Habsieger(
Book
)
1 edition published in 1986 in French and held by 8 WorldCat member libraries worldwide
1 edition published in 1986 in French and held by 8 WorldCat member libraries worldwide
Leçons de mathématiques d'aujourd'hui(
Book
)
in French and held by 6 WorldCat member libraries worldwide
in French and held by 6 WorldCat member libraries worldwide
Leçons de mathématiques d'aujourd'hui(
Book
)
1 edition published in 2003 in French and held by 3 WorldCat member libraries worldwide
1 edition published in 2003 in French and held by 3 WorldCat member libraries worldwide
Exercices corrigés de mathématiques (options M, P) posés à l'oral des concours ENSI solutions proposées by
Laurent Habsieger(
Book
)
in French and held by 3 WorldCat member libraries worldwide
in French and held by 3 WorldCat member libraries worldwide
Aspects explicites des fonctions L et applications by
Charlotte Euvrard(
)
2 editions published in 2016 in French and held by 2 WorldCat member libraries worldwide
This thesis focuses on Lfunctions, their explicit aspects and their applications.In the first chapter, we give a precise definition of Lfunctions and their main properties, especially about the invariants called local parameters. Then, we deal with Artin Lfunctions. For them, we have created a computer program in PARI/GP which gives the coefficients and the invariants for an Artin Lfunction above Q.In the second chapter, we make explicit a theorem of Henryk Iwaniec and Emmanuel Kowalski, which distinguishes between two Lfunctions by considering their local parameters for primes up to a theoretical bound.Actually, distinguishing between sums of local parameters of Artin Lfunctions is the same as separating the associated characters by the Frobenius automorphism. This is the subject of the third chapter, that can be related to Chebotarev Theorem. By applying the result to conjugate characters of the alternating group, we get a bound for a prime p giving the factorization modulo $p$ of a certain polynomial. This work has to be compared with a result from Joël Bellaïche (2013).Finally, we numerically illustrate our results by studying the evolution of the bound on polynomials X^n+uX+v, for n=5, 7 and 13
2 editions published in 2016 in French and held by 2 WorldCat member libraries worldwide
This thesis focuses on Lfunctions, their explicit aspects and their applications.In the first chapter, we give a precise definition of Lfunctions and their main properties, especially about the invariants called local parameters. Then, we deal with Artin Lfunctions. For them, we have created a computer program in PARI/GP which gives the coefficients and the invariants for an Artin Lfunction above Q.In the second chapter, we make explicit a theorem of Henryk Iwaniec and Emmanuel Kowalski, which distinguishes between two Lfunctions by considering their local parameters for primes up to a theoretical bound.Actually, distinguishing between sums of local parameters of Artin Lfunctions is the same as separating the associated characters by the Frobenius automorphism. This is the subject of the third chapter, that can be related to Chebotarev Theorem. By applying the result to conjugate characters of the alternating group, we get a bound for a prime p giving the factorization modulo $p$ of a certain polynomial. This work has to be compared with a result from Joël Bellaïche (2013).Finally, we numerically illustrate our results by studying the evolution of the bound on polynomials X^n+uX+v, for n=5, 7 and 13
Études combinatoires sur les permutations et partitions d'ensemble by
Anisse Kasraoui(
Book
)
2 editions published in 2009 in French and held by 2 WorldCat member libraries worldwide
This thesis consists of four chapters, each on a different topic in enumerative combinatorics, all related in some way to the enumeration of permutations or set partitions. In the first chapter, we prove and generalize Steingrimsson's conjectures on EulerMahonian statistics on ordered set partitions. In the second chapter, we introduce and study a new class of statistics on words: the "majinv" statistics. These are graphical interpolation of the wellknown "major index" and "inversion number".In the third chapter, we show that the joint distribution of the numbers of crossings and nestings on set partitions is symmetric. We also put this result in the larger context of enumeration of increasing and decreasing chains in 01fillings of moon polyominoes.In the last chapter, we decribe various aspects of the AlSalamChihara qLaguerre polynomials. These include combinatorial descriptions of the polynomials, the moments, the orthogonality relation and a combinatorial interpretation of the linearization coefficients
2 editions published in 2009 in French and held by 2 WorldCat member libraries worldwide
This thesis consists of four chapters, each on a different topic in enumerative combinatorics, all related in some way to the enumeration of permutations or set partitions. In the first chapter, we prove and generalize Steingrimsson's conjectures on EulerMahonian statistics on ordered set partitions. In the second chapter, we introduce and study a new class of statistics on words: the "majinv" statistics. These are graphical interpolation of the wellknown "major index" and "inversion number".In the third chapter, we show that the joint distribution of the numbers of crossings and nestings on set partitions is symmetric. We also put this result in the larger context of enumeration of increasing and decreasing chains in 01fillings of moon polyominoes.In the last chapter, we decribe various aspects of the AlSalamChihara qLaguerre polynomials. These include combinatorial descriptions of the polynomials, the moments, the orthogonality relation and a combinatorial interpretation of the linearization coefficients
Some questions in combinatorial and elementary number theory by
Salvatore Tringali(
)
1 edition published in 2013 in English and held by 1 WorldCat member library worldwide
This thesis is divided into two parts. Part I is about additive combinatorics. Part II deals with questions in elementary number theory. In Chapter 1, we generalize the Davenport transform to prove that if si S\mathbb A=(A, +)S is acancellative semigroup (either abelian or not) and SX, YS are nonempty subsets of SAS such that the subsemigroup generated by SYS is abelian, then SSX+Y\gc\min(\gamma(Y, X+YI)SS, where for SZ\subsetcq AS we let S\gamma(Z):=\sup_{z_0\in Z^\times}\in f_(z_0\nc z\inZ) (vm ord)(zz_0)S. This implies an extension of Chowla's and Pillai's theorems for cyclic groups and a stronger version of an addition theorem by Hamidoune and Karolyi for arbitrary groups. In Chapter 2, we show that if S(A, +) is a cancellative semigroup and SX, Y\subsetcq AS then SSX+Y\gc\min(\gammaX+Y), X+YI)SS. This gives a generalization of Kemperman's inequality for torsion free groups and a stronger version of the HamidouneKarolyi theorem. In Chapter 3, we generalize results by Freiman et al. by proving that if S(A,\ctlot)S is a linearly orderable semigroup and SSS is a finite subset of SAS generating a nonabelian subsemigroup, then SS^2\gc3S2S. In Chapter 4, we prove results related to conjecture by Gyory and Smyth on the sets SR_k^\pm(a,b)S of all positive integers SnS such that Sn^kS divides Sa^a \pmb^nS for fixed integers SaS, SbS and SkS with Sk\gc3S, Sab\gc2Set S\gcd(a,b) = 1S. In particular, we show that SR_k^pm(a,b)S is finite if Sk\gc\max(a.b)S. In Chapter 5, we consider a question on primes and divisibility somchow related to Znam's problem and the AgohGiuga conjecture
1 edition published in 2013 in English and held by 1 WorldCat member library worldwide
This thesis is divided into two parts. Part I is about additive combinatorics. Part II deals with questions in elementary number theory. In Chapter 1, we generalize the Davenport transform to prove that if si S\mathbb A=(A, +)S is acancellative semigroup (either abelian or not) and SX, YS are nonempty subsets of SAS such that the subsemigroup generated by SYS is abelian, then SSX+Y\gc\min(\gamma(Y, X+YI)SS, where for SZ\subsetcq AS we let S\gamma(Z):=\sup_{z_0\in Z^\times}\in f_(z_0\nc z\inZ) (vm ord)(zz_0)S. This implies an extension of Chowla's and Pillai's theorems for cyclic groups and a stronger version of an addition theorem by Hamidoune and Karolyi for arbitrary groups. In Chapter 2, we show that if S(A, +) is a cancellative semigroup and SX, Y\subsetcq AS then SSX+Y\gc\min(\gammaX+Y), X+YI)SS. This gives a generalization of Kemperman's inequality for torsion free groups and a stronger version of the HamidouneKarolyi theorem. In Chapter 3, we generalize results by Freiman et al. by proving that if S(A,\ctlot)S is a linearly orderable semigroup and SSS is a finite subset of SAS generating a nonabelian subsemigroup, then SS^2\gc3S2S. In Chapter 4, we prove results related to conjecture by Gyory and Smyth on the sets SR_k^\pm(a,b)S of all positive integers SnS such that Sn^kS divides Sa^a \pmb^nS for fixed integers SaS, SbS and SkS with Sk\gc3S, Sab\gc2Set S\gcd(a,b) = 1S. In particular, we show that SR_k^pm(a,b)S is finite if Sk\gc\max(a.b)S. In Chapter 5, we consider a question on primes and divisibility somchow related to Znam's problem and the AgohGiuga conjecture
L'enseignement de l'arithmétique en France au collège et à la transition collège / lycée by
Maha Majaj(
)
1 edition published in 2011 in French and held by 1 WorldCat member library worldwide
In this research, we are interested in a didactic study of the arithmetical contents, where arithmetic refers to elementary theory of numbers. We aimed to study choices of the teaching of arithmetic in France from the early XXth century and to identify institutional constraints for the reintroduction of arithmetic in the secondary education that occurred in the early XXIth and their effects on teaching practices and students' experiences. First, we lead an epistemological analysis to describe the different mathematical organizations, and definitions that should be chosen for the teaching of arithmetic that we have completed with a review of previous researches in the AngloSaxon world on one hand, and in the French works on the other hand. We lead then an institutional analysis of the arithmetic in an ecological perspective to reveal different systems of constraints and conditions that should have an influence on the evolutions of this knowledge during the process of internal didactic transposition, by analyzing the programs and the textbooks in two institutions: Middle school and the fifth year of High school, from the reform of 1902 till 2010, tracking the mathematical organizations and the definitions. Second, we lead a study of the personal relationships of teachers and students regarding the arithmetical concepts involved in fifth year of high school through two questionnaires, including a comparison between teachers' answers and the answers of their own pupils. A main result of our research is the great instability of the arithmetical content in the French curriculum at Middle school and at the transition from Middle school into High school
1 edition published in 2011 in French and held by 1 WorldCat member library worldwide
In this research, we are interested in a didactic study of the arithmetical contents, where arithmetic refers to elementary theory of numbers. We aimed to study choices of the teaching of arithmetic in France from the early XXth century and to identify institutional constraints for the reintroduction of arithmetic in the secondary education that occurred in the early XXIth and their effects on teaching practices and students' experiences. First, we lead an epistemological analysis to describe the different mathematical organizations, and definitions that should be chosen for the teaching of arithmetic that we have completed with a review of previous researches in the AngloSaxon world on one hand, and in the French works on the other hand. We lead then an institutional analysis of the arithmetic in an ecological perspective to reveal different systems of constraints and conditions that should have an influence on the evolutions of this knowledge during the process of internal didactic transposition, by analyzing the programs and the textbooks in two institutions: Middle school and the fifth year of High school, from the reform of 1902 till 2010, tracking the mathematical organizations and the definitions. Second, we lead a study of the personal relationships of teachers and students regarding the arithmetical concepts involved in fifth year of high school through two questionnaires, including a comparison between teachers' answers and the answers of their own pupils. A main result of our research is the great instability of the arithmetical content in the French curriculum at Middle school and at the transition from Middle school into High school
Conjecture n! et généralisations by
JeanChristophe Aval(
Book
)
in French and held by 1 WorldCat member library worldwide
Cette thèse est consacrée au problème de combinatoire algébrique appelée conjecture n!. Plus explicitement, on étudie la structure de certains espaces notés Mu et indexés par les partitions u de l'entier n. Chaque espace Mu est le cône de dérivation d'un polynôme Delta u, généralisant en deux alphabets le déterminant de Vandermonde. Le coeur de ce travail, motivé par l'interprétation de certains polynômes de Macdonald en termes de multiplicité des représentations irréductibles du Snmodule Mu, est la conjecture n!, énoncée en 1991 par A. Garsia et M. Haiman et récemment prouvée par ce dernier. On s'intéresse ici tout d'abord à l'explicitation de bases monomiales des espaces Mu. Cette approche est très liée à l'étude de l'idéal annulateur de Delta u, et nous conduit à introduire certains opérateurs de dérivation, dits "opérateurs de sauts." On obtient une base monomiale explicite et une description de l'idéal annulateur pour les partitions en équerres, et pour le sousespace en un alphabet Mu(X) avec une partition u quelconque. Les opérateurs de sauts se révèlent cruciaux pour l'introduction et l'étude de généralisations de la conjecture n!. Dans le cas des partitions trouées (approche récursive de la conjecture n!), l'obtention d'une base explicite du sousespace en un alphabet permet de traiter une spécialisation de la fondamentale "récurrence à quatre termes". Dans le cas des diagrammes à plusieurs trous, l'introduction de sommes de cônes de dérivation permet d'énoncer une conjecture généralisant la conjecture n!, supportée par l'obtention d'une borne supérieure et la structure du sousespace en un alphabet
in French and held by 1 WorldCat member library worldwide
Cette thèse est consacrée au problème de combinatoire algébrique appelée conjecture n!. Plus explicitement, on étudie la structure de certains espaces notés Mu et indexés par les partitions u de l'entier n. Chaque espace Mu est le cône de dérivation d'un polynôme Delta u, généralisant en deux alphabets le déterminant de Vandermonde. Le coeur de ce travail, motivé par l'interprétation de certains polynômes de Macdonald en termes de multiplicité des représentations irréductibles du Snmodule Mu, est la conjecture n!, énoncée en 1991 par A. Garsia et M. Haiman et récemment prouvée par ce dernier. On s'intéresse ici tout d'abord à l'explicitation de bases monomiales des espaces Mu. Cette approche est très liée à l'étude de l'idéal annulateur de Delta u, et nous conduit à introduire certains opérateurs de dérivation, dits "opérateurs de sauts." On obtient une base monomiale explicite et une description de l'idéal annulateur pour les partitions en équerres, et pour le sousespace en un alphabet Mu(X) avec une partition u quelconque. Les opérateurs de sauts se révèlent cruciaux pour l'introduction et l'étude de généralisations de la conjecture n!. Dans le cas des partitions trouées (approche récursive de la conjecture n!), l'obtention d'une base explicite du sousespace en un alphabet permet de traiter une spécialisation de la fondamentale "récurrence à quatre termes". Dans le cas des diagrammes à plusieurs trous, l'introduction de sommes de cônes de dérivation permet d'énoncer une conjecture généralisant la conjecture n!, supportée par l'obtention d'une borne supérieure et la structure du sousespace en un alphabet
Une étude de deux problèmes diophantiens by
Nicolas Brisebarre(
Book
)
1 edition published in 1998 in French and held by 1 WorldCat member library worldwide
CETTE THESE EST COMPOSEE DE DEUX CHAPITRES INDEPENDANTS TRAITANT DE PROBLEMES LIES A L'APPROXIMATION DIOPHANTIENNE. DANS LA PREMIERE PARTIE DE CE MEMOIRE, NOUS PROPOSONS UNE NOUVELLE APPROCHE ET UNE GENERALISATION DE RESULTATS CARACTERISANT LES FONCTIONS ENTIERES SOLUTIONS DE SYSTEMES DE DEUX EQUATIONS AUX DIFFERENCES FINIES. NOUS DONNONS, EN OUTRE, UN ALGORITHME, IMPLANTE EN MAPLE, QUI PERMET DE TROUVER LA FORME EXPLICITE DES SOLUTIONS. PUIS, DANS UNE SECONDE PARTIE, NOUS UNIFIONS, A L'AIDE DE L'ETUDE D'UNE CLASSE DE POLYNOMES GENERALISANT LES POLYNOMES DE LEGENDRE, DES TRAVAUX ANTERIEURS D'E. A. RUKHADZE, A. DUBITSKAS, M. HATA, D. V. ET G. V. CHUDNOVSKY SUR LES RECHERCHES DE MESURES D'IRRATIONALITE DE LOG2 ET /3
1 edition published in 1998 in French and held by 1 WorldCat member library worldwide
CETTE THESE EST COMPOSEE DE DEUX CHAPITRES INDEPENDANTS TRAITANT DE PROBLEMES LIES A L'APPROXIMATION DIOPHANTIENNE. DANS LA PREMIERE PARTIE DE CE MEMOIRE, NOUS PROPOSONS UNE NOUVELLE APPROCHE ET UNE GENERALISATION DE RESULTATS CARACTERISANT LES FONCTIONS ENTIERES SOLUTIONS DE SYSTEMES DE DEUX EQUATIONS AUX DIFFERENCES FINIES. NOUS DONNONS, EN OUTRE, UN ALGORITHME, IMPLANTE EN MAPLE, QUI PERMET DE TROUVER LA FORME EXPLICITE DES SOLUTIONS. PUIS, DANS UNE SECONDE PARTIE, NOUS UNIFIONS, A L'AIDE DE L'ETUDE D'UNE CLASSE DE POLYNOMES GENERALISANT LES POLYNOMES DE LEGENDRE, DES TRAVAUX ANTERIEURS D'E. A. RUKHADZE, A. DUBITSKAS, M. HATA, D. V. ET G. V. CHUDNOVSKY SUR LES RECHERCHES DE MESURES D'IRRATIONALITE DE LOG2 ET /3
Leçons de mathématiques d'aujourd'hui II(
Book
)
1 edition published in 2003 in French and held by 1 WorldCat member library worldwide
1 edition published in 2003 in French and held by 1 WorldCat member library worldwide
On the NymanBeurling criterion for the Riemann hypothesis by
Laurent Habsieger(
)
1 edition published in 2007 in English and held by 1 WorldCat member library worldwide
1 edition published in 2007 in English and held by 1 WorldCat member library worldwide
The fourth moment of automorphic Lfunctions at prime power level by
Olga Balkanova(
)
1 edition published in 2015 in English and held by 1 WorldCat member library worldwide
The main result of this dissertation is an asymptotic formula for the fourth moment of automorphic Lfunctions of prime power level p, vx. This is a continuation of the work of Rouymi, who computed the first three moments at prime power level, and a generalisation of results obtained for prime level by Duke, Friedlander & Iwaniec and Kowalski, Michel & Vanderkam
1 edition published in 2015 in English and held by 1 WorldCat member library worldwide
The main result of this dissertation is an asymptotic formula for the fourth moment of automorphic Lfunctions of prime power level p, vx. This is a continuation of the work of Rouymi, who computed the first three moments at prime power level, and a generalisation of results obtained for prime level by Duke, Friedlander & Iwaniec and Kowalski, Michel & Vanderkam
Exercices corrigés de mathématiques posés à l'oral des concours ENSI. options M, P by
Laurent Habsieger(
Book
)
2 editions published in 1986 in French and held by 1 WorldCat member library worldwide
2 editions published in 1986 in French and held by 1 WorldCat member library worldwide
Conjecture de brumerstark non abélienne by
Gaëlle Dejou(
)
1 edition published in 2011 in French and held by 1 WorldCat member library worldwide
Finding annihilators of the ideal class group of an abelian extension of Q is a classical subject which goes back to work of Kummer and Stickelberger. The BrumerStark conjecture deals with abelian extensions of number fields and predicts that a group ring element, called the BrumerStickelberger element, annihilates the ideal class group of the extension under consideration. Moreover it specifies that the generators thus obtained have special properties. The aim of this work is to generalize this conjecture to nonabelian Galois extensions. We first focus on the study of a nonabelian analogue of the Brumer element, necessary to establish a nonabelian generalization of the conjecture. The second part is devoted to the statement of our nonabelian conjecture, and the properties it satisfies. We are particularly interested in extension change properties. We then study the specific case of extensions whose Galois group has an abelian normal subgroup H of prime index. If the BrumerStark conjecture associated to certain abelian subextensions holds, we prove two results according to the parity of the cardinal of H : in the odd case, we get the nonabelian BrumerStark conjecture, and in the even case, we establish an abelianity result implying under additional hypotheses the proof of the nonabelian conjecture. Thanks to PARIGP, we finally do some numerical verifications of the nonabelian conjecture, proving its validity in the tested examples
1 edition published in 2011 in French and held by 1 WorldCat member library worldwide
Finding annihilators of the ideal class group of an abelian extension of Q is a classical subject which goes back to work of Kummer and Stickelberger. The BrumerStark conjecture deals with abelian extensions of number fields and predicts that a group ring element, called the BrumerStickelberger element, annihilates the ideal class group of the extension under consideration. Moreover it specifies that the generators thus obtained have special properties. The aim of this work is to generalize this conjecture to nonabelian Galois extensions. We first focus on the study of a nonabelian analogue of the Brumer element, necessary to establish a nonabelian generalization of the conjecture. The second part is devoted to the statement of our nonabelian conjecture, and the properties it satisfies. We are particularly interested in extension change properties. We then study the specific case of extensions whose Galois group has an abelian normal subgroup H of prime index. If the BrumerStark conjecture associated to certain abelian subextensions holds, we prove two results according to the parity of the cardinal of H : in the odd case, we get the nonabelian BrumerStark conjecture, and in the even case, we establish an abelianity result implying under additional hypotheses the proof of the nonabelian conjecture. Thanks to PARIGP, we finally do some numerical verifications of the nonabelian conjecture, proving its validity in the tested examples
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 Charpentier, Eric Editor
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 Godefroy, Gilles
 MartelGolse, Valérie
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 Gritzmann, Peter Author
 Klee, Victor
 Cartier, Pierre Mathématicien
 Kahane, JeanPierre
 Université de Bordeaux I. Ecole doctorale de mathématiques et informatique Degree grantor
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