Plongement d'une extension d'ordre p ou p2 dans une surextension non abelienne d'ordre p3.
Plongement d'une extension qudratique dans une extension quaternionienne.
Plongements kummériens dans les -extensions
Plongements -adiques et -nombres de Weil
Nous introduisons la notion de nombre de Weil -adique par analogie avec la notion classique de nombre de Weil à l’infini ; et nous en étudions quelques propriétés en liaison avec les plongements et les valeurs absolues réelles ou -adiques des corps de nombres. En appendice, nous en tirons diverses applications à la théorie d’Iwasawa des tours cyclotomiques.
Poincaré Series on GL (r) and Kloostermann Sums.
Points of Order p on Elliptic Curves Over Q(...p).
Points on Shimura curves rational over number fields.
Points périodiques des automorphismes affines.
Points rationnels des courbes modulaires
Pólya fields and Pólya numbers
A number field , with ring of integers , is said to be a Pólya field if the -algebra formed by the integer-valued polynomials on admits a regular basis. In a first part, we focus on fields with degree less than six which are Pólya fields. It is known that a field is a Pólya field if certain characteristic ideals are principal. Analogously to the classical embedding problem, we consider the embedding of in a Pólya field. We give a positive answer to this embedding problem by showing that...
Pólya fields, Pólya groups and Pólya extensions: a question of capitulation
A number field , with ring of integers , is said to be a Pólya field when the -algebra formed by the integer-valued polynomials on admits a regular basis. It is known that such fields are characterized by the fact that some characteristic ideals are principal. Analogously to the classical embedding problem in a number field with class number one, when is not a Pólya field, we are interested in the embedding of in a Pólya field. We study here two notions which can be considered as measures...
Polylogarithmes
Polynome mit nicht durch Restklassen beschreibbaren Primteilermengen
Polynômes à groupe de Galois diédral
Soit un corps et une extension quadratique de . Étant donné un polynôme de à groupe de Galois cyclique, nous donnons une méthode pour construire un polynôme de à groupe de Galois diédral, à partir des racines de . Cette méthode est tout à fait explicite : nous donnons de nombreux exemples de polynômes à groupe de Galois diédral sur le corps .
Polynômes à valeurs entières
Polynomial cycles in certain rings of rationals
It is shown that the methods established in [HKN3] can be effectively used to study polynomial cycles in certain rings. We shall consider the rings and shall describe polynomial cycles in the case when is either odd or twice a prime.
Polynomial mappings defined by forms with a common factor
Polynomial relations amongst algebraic units of low measure
For an algebraic number field and a subset , we establish a lower bound for the average of the logarithmic heights that depends on the ideal of polynomials in vanishing at the point .
Polynomials and degrees of maps in real normed algebras
Let be the algebra of quaternions or octonions . In this manuscript an elementary proof is given, based on ideas of Cauchy and D’Alembert, of the fact that an ordinary polynomial has a root in . As a consequence, the Jacobian determinant is always non-negative in . Moreover, using the idea of the topological degree we show that a regular polynomial over has also a root in . Finally, utilizing multiplication () in , we prove various results on the topological degree of products...
Polynomials and Vandermonde matrices over the field of quaternions.