Quadratische Formen und die Artin-Schreiersche Theorie der formal reellen Körper
Quadratische Formen und Monodromiegruppen von Singularitäten.
Quadratische Formen und quadratische Reziprozitätsgesetze über algebraischen Zahlkörpern.
Quadratische Räume mit zwei Unterräumen.
Quadratische Räume unendlicher Dimension und partielle Isomorphismen.
Quadratsummen in totalreellen algebraischen Zahlkörpern.
Quasi-additive functions.
Quelques formules concernant la théorie de la fonction [x] et des nombres de Bernoulli. (Extrait d'une lettre adressée à K. Hensel).
Quelques problèmes des formes quadratiques sur les corps
Quelques propriétés d’approximation reliées à la cohomologie galoisienne d’un groupe algébrique fini
On étudie différentes propriétés d’approximation pour des espaces homogènes (à stabilisateur fini) de sur un corps de nombres. On discute également du lien avec le problème de Galois inverse et on établit une formule pour le groupe de Brauer non ramifié de .
Quelques questions d’approximation faible pour les tores algébriques
Soient un corps global, un -tore, un ensemble fini de places de . On note le complété de en . Soit , resp. , le groupe des points -rationnels, resp. -rationnels, de . Notons le sous-groupe compact maximal. Nous montrons que pour et convenables l’application induite par l’application diagonale n’est pas surjective. Cela implique que pour convenable le groupe ne couvre pas forcément toutes les classes de -équivalence de . Lorsque est un corps de fonctions d’une variable...
Quelques remarques sur le -invariant
Quotients of index two and general quotients in a space of orderings
We investigate quotient structures and quotient spaces of a space of orderings arising from subgroups of index two. We provide necessary and sufficient conditions for a quotient structure to be a quotient space that, among other things, depend on the stability index of the given space. The case of the space of orderings of the field ℚ(x) is particularly interesting, since then the theory developed simplifies significantly. A part of the theory firstly developed for quotients of index 2 generalizes...
Quotients of Theta Series as Rational Functions of J and ?.
Ramanujan identities and Euler products for a type of Dirichlet series
Ramification in p-Adic Lie Extensions.
Random Thue and Fermat equations
We consider Thue equations of the form , and assuming the truth of the abc-conjecture, we show that almost all locally soluble Thue equations of degree at least three violate the Hasse principle. A similar conclusion holds true for Fermat equations of degree at least six.
Rational base number systems for p-adic numbers
This paper deals with rational base number systems for p-adic numbers. We mainly focus on the system proposed by Akiyama et al. in 2008, but we also show that this system is in some sense isomorphic to some other rational base number systems by means of finite transducers. We identify the numbers with finite and eventually periodic representations and we also determine the number of representations of a given p-adic number.
Rational base number systems for p-adic numbers
This paper deals with rational base number systems for p-adic numbers. We mainly focus on the system proposed by Akiyama et al. in 2008, but we also show that this system is in some sense isomorphic to some other rational base number systems by means of finite transducers. We identify the numbers with finite and eventually periodic representations and we also determine the number of representations of a given p-adic number.
Rational congruence for uniform multiplicative designs.