Die Kombinationen gegebenen Profils. II
Die Kombinationen gegebenen Profils. III
Die Stufe von Ordnungen ganzer Zahlen in algebraischen Zahlkörpern.
Die Zerlegungscharaktere abelscher total reeller Erweiterungen reeller Funktionenkörper einer Variablen.
Dimensions of anisotropic indefinite quadratic forms. I.
Dimensions of anisotropic indefinite quadratic forms. II.
Discriminant Sets of Families of Hyperbolic Polynomials of Degree 4 and 5
∗ Research partially supported by INTAS grant 97-1644A real polynomial of one real variable is hyperbolic (resp. strictly hyperbolic) if it has only real roots (resp. if its roots are real and distinct). We prove that there are 116 possible non-degenerate configurations between the roots of a degree 5 strictly hyperbolic polynomial and of its derivatives (i.e. configurations without equalities between roots). The standard Rolle theorem allows 286 such configurations. To obtain the result we study...
Discussion de la fraction
Divisibilité du nombre de classes des corps abéliens réels.
Divisionsalgebren über Funktionenkörpern
Eine Bemerkung über die Wurzelpolynome Galoisscher Gleichungen.
Eine Bemerkung zu den höheren Pythagoraszahlen reeller Körper.
Eine Bemerkung zum Aufsatz "Der Fundamentalsatz der Algebra und der Intuitionismus" von H. Kneser.
Equations with equivalent roots
Erblich euklidische Körper.
Errata to "On the fundamental theorem of algebra" (COLLOQ. MATH. 73 (1997), 193-194)
Estensioni di una struttura paracomplessa su un corpo algebricamente chiuso ad un suo ampliamento trascendente semplice
Étienne Bézout : analyse algébrique au siècle des lumières
Le but de cet article, à travers l’étude des travaux en analyse algébrique finie d’Étienne Bézout (1730-1783), est de mieux faire connaître ses résultats, tels qu’il les a effectivement trouvés, et de mettre en valeur aussi bien les points de vue novateurs que les méthodes originales, mis en œuvre à cet effet. L’idée de ramener le problème de l’élimination d’une ou plusieurs inconnues à l’étude d’un système d’équations du premier degré, son utilisation inhabituelle des coefficients indéterminés...
Euklidische Körper und euklidische Hüllen von Körpern.
Even and Old Overdetermined Strata for Degree 6 Hyperbolic Polynomials
2000 Mathematics Subject Classification: 12D10.In the present paper we consider degree 6 hyperbolic polynomials (HPs) in one variable (i.e. real and with all roots real). We are interested in such HPs whose number of equalities between roots of the polynomial and/or its derivatives is higher than expected. We give the complete study of the four families of such degree 6 even HPs and also of HPs which are primitives of degree 5 HPs.Research partially supported by research project 20682 for cooperation...