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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...

Tamely ramified extensions's structure.

Ibadula, Denis (2001)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

Ternary rings of Pappian planes

Libuše Marková (1976)

Sborník prací Přírodovědecké fakulty University Palackého v Olomouci. Matematika

The absolute Galois group of a pseudo p-adically closed field.

Moshe Jarden, Dan Haran (1988)

Journal für die reine und angewandte Mathematik

The absolute Galois group of a pseudo real closed field

Dan Haran, Moshe Jarden (1985)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

The algebraic closure of a $p$ -adic number field is a complete topological field

José E. Marcos (2006)

Mathematica Slovaca

The Algebraic nature of the elementary theory of PRC fields.

Moshe Jarden (1988)

Manuscripta mathematica

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 constants of the Volterra derivation

Pál Hegedűs (2012)

Open Mathematics

The ring of constants of the Volterra derivation is found. Confirming a conjecture of Zielinski, it is always a polynomial ring.

The differential equation y' = fy in the algebras H(D).

Alain Escassut, Marie-Claude Sarmant (1988)

Collectanea Mathematica

The differential Galois theory of regular singular p-adic differential equations.

Richard Crew (1996)

Mathematische Annalen

The differential spectrum of a ring

Paulo Ribenboim (1973)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

The distributivity property of finite intersections of valuation rings

Ján Mináč (1984)

Mathematica Slovaca

The effect on associated prime ideals produced by an extension of the base field.

Rodney Y. Sharp (1976)

Mathematica Scandinavica

The Elementary Theory of Algebraic Fields of Finite Corank.

Moshe Jarden, Ursel Kiehne (1975)

Inventiones mathematicae

The Elementary Theory of co-Free Ax Fields

M. Jarden (1976)

Inventiones mathematicae

The equation $y^{'} = f y$ in $ℂ_{p}$ when $f$ is quasi-invertible

Alain Escassut (1991)

Rendiconti del Seminario Matematico della Università di Padova

The factorization of certain quadrinominals.

W.H. Mills (1985)

Mathematica Scandinavica

The factorization of $f (x) x^{n} + g (x)$ with $f (x)$ monic and of degree $\leq 2$ .

Joshua Harrington, Andrew Vincent, Daniel White (2013)

Journal de Théorie des Nombres de Bordeaux

In this paper we investigate the factorization of the polynomials $f (x) x^{n} + g (x) \in ℤ [x]$ 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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