Pentes des Fibrés Vectoriels Adéliques sur un Corps Global
Perfect Gaussian integers
Period of a linear recurrence
Period Polynomials for Generalized cyclotomic periods.
Periodic expansions and units in quadratic and cubic number fields.
Periodic Gaussian moats.
Periodic Jacobi-Perron expansions associated with a unit
We prove that, for any unit in a real number field of degree , there exits only a finite number of n-tuples in which have a purely periodic expansion by the Jacobi-Perron algorithm. This generalizes the case of continued fractions for . For we give an explicit algorithm to compute all these pairs.
Periodic points, multiplicities, and dynamical units.
Periods of sets of lengths: a quantitative result and an associated inverse problem
The investigation of quantitative aspects of non-unique factorizations in the ring of integers of an algebraic number field gives rise to combinatorial problems in the class group of this number field. In this paper we investigate the combinatorial problems related to the function 𝓟(H,𝓓,M)(x), counting elements whose sets of lengths have period 𝓓, for extreme choices of 𝓓. If the class group meets certain conditions, we obtain the value of an exponent in the asymptotic formula of this function...
Petits discriminants
Petits discriminants
On construit des corps de nombres de petits discriminants relativement aux minorations de Odlyzko.
Pfaffien et discriminant
Pfister's Dimension and the Level of Fields.
Piatetski-Shapiro meets Chebotarev
Let K be a finite Galois extension of the field ℚ of rational numbers. We prove an asymptotic formula for the number of Piatetski-Shapiro primes not exceeding a given quantity for which the associated Frobenius class of automorphisms coincides with any given conjugacy class in the Galois group of K/ℚ. In particular, this shows that there are infinitely many Piatetski-Shapiro primes of the form a² + nb² for any given natural number n.
Pisot Sequences.
Pisot sequences which satisfy no linear recurrence II
Plongeants d'extensions galoisiennes
Plongement d'extensions diédrales.
Plongement d'une extension de degré p2 dans une surextension non abélienne de degré p3: étude locale-globale.
Plongement d'une extension diédrale dans une extension diédrale ou quaternionienne
On utilise les méthodes de Neukirch et Poitou pour écrire les conditions locales et globales des problèmes de plongement. Le cas étudié ici est celui du plongement d’une extension diédrale dans une extension diédrale ou quaternionienne, le corps de base étant un corps de nombres.