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T -filtres, ensembles analytiques et transformation de Fourier P -adique

Alain Escassut (1975)

Annales de l'institut Fourier

Les propriétés des éléments analytiques sur une partie D d’un corps ultramétrique complet, algébriquement clos, dépendent de l’existence sur D de filtres strictement annulateurs que l’on caractérise par des relations arithmétiques entre les diamètres et les distances mutuelles des trous de D grâce à la notion de T -filtre. Alors les ensembles analytiques sont les ensembles sans T -filtre à plage non vide. D’autre part, le problème de la transformation de Fourier p -adique se ramène à un problème d’analycité...

The arithmetic of curves defined by iteration

Wade Hindes (2015)

Acta Arithmetica

We show how the size of the Galois groups of iterates of a quadratic polynomial f can be parametrized by certain rational points on the curves Cₙ: y² = fⁿ(x) and their quadratic twists (here fⁿ denotes the nth iterate of f). To that end, we study the arithmetic of such curves over global and finite fields, translating key problems in the arithmetic of polynomial iteration into a geometric framework. This point of view has several dynamical applications. For instance, we establish a maximality theorem...

The Boolean space of higher level orderings

Katarzyna Osiak (2007)

Fundamenta Mathematicae

Let K be an ordered field. The set X(K) of its orderings can be topologized to make it a Boolean space. Moreover, it has been shown by Craven that for any Boolean space Y there exists a field K such that X(K) is homeomorphic to Y. Becker's higher level ordering is a generalization of the usual concept of ordering. In a similar way to the case of ordinary orderings one can define a topology on the space of orderings of fixed exact level. We show that it need not be Boolean. However, our main theorem...

The factorization of f ( x ) x n + g ( x ) with f ( x ) monic and of degree ≤ 2 .

Joshua Harrington, Andrew Vincent, Daniel White (2013)

Journal de Théorie des Nombres de Bordeaux

In this paper we investigate the factorization of the polynomials f ( x ) x n + g ( x ) ∈ ℤ [ x ] in the special case where f ( x ) is a monic quadratic polynomial with negative discriminant. We also mention similar results in the case that f ( x ) is monic and linear.

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