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Applications de la notion d'entropie au développement d'un nombre réel dans une base de Pisot

Anne Bertrand-Mathis (1985)

Annales de l'institut Fourier

Soit θ un nombre de Pisot de degré s  ; nous avons montré précédemment que l’endomorphisme du tore T s dont θ est valeur propre est facteur du θ -shift bilatéral par une application continue q s  ; nous prouvons ici (théorème 1) que l’application q s conserve l’entropie de toute mesure invariante sur le θ -shift. Ceci permet de définir l’entropie d’un nombre dans la base θ et d’en étudier la stabilité. Nous généralisons également des résultats de Kamae, Rauzy et Bernay.

Applications of spinor class fields: embeddings of orders and quaternionic lattices

Luis Arenas-Carmona (2003)

Annales de l'Institut Fourier

We extend the theory of spinor class fields and relative spinor class fields to study representation problems in several classical linear algebraic groups over number fields. We apply this theory to study the set of isomorphism classes of maximal orders of central simple algebras containing a given maximal Abelian suborder. We also study isometric embeddings of one skew-Hermitian Quaternionic lattice into another.

Approximatting rings of integers in number fields

J. A. Buchmann, H. W. Lenstra (1994)

Journal de théorie des nombres de Bordeaux

In this paper we study the algorithmic problem of finding the ring of integers of a given algebraic number field. In practice, this problem is often considered to be well-solved, but theoretical results indicate that it is intractable for number fields that are defined by equations with very large coefficients. Such fields occur in the number field sieve algorithm for factoring integers. Applying a variant of a standard algorithm for finding rings of integers, one finds a subring of the number field...

Arithmetic Hilbert modular functions (II).

Walter L. Baily Jr. (1985)

Revista Matemática Iberoamericana

The purpose of this paper, which is a continuation of [2, 3], is to prove further results about arithmetic modular forms and functions. In particular we shall demonstrate here a q-expansion principle which will be useful in proving a reciprocity law for special values of arithmetic Hilbert modular functions, of which the classical results on complex multiplication are a special case. The main feature of our treatment is, perhaps, its independence of the theory of abelian varieties.

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