All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 85 Next

Displaying 1681 – 1700 of 1964

Showing per page

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...

Arakelov computations in genus 3 curves

Jordi Guàrdia (2001)

Journal de théorie des nombres de Bordeaux

Arakelov invariants of arithmetic surfaces are well known for genus 1 and 2 ([4], [2]). In this note, we study the modular height and the Arakelov self-intersection for a family of curves of genus 3 with many automorphisms: C n : Y 4 = X 4 - ( 4 n - 2 ) X 2 Z 2 + Z 4 . Arakelov calculus involves both analytic and arithmetic computations. We express the periods of the curve C n in terms of elliptic integrals. The substitutions used in these integrals provide a splitting of the jacobian of C n as a product of three elliptic curves. Using the corresponding...

ARI/GARI, la dimorphie et l'arithmétique des multizêtas : un premier bilan

Jean Ecalle (2003)

Journal de théorie des nombres de Bordeaux

Nous tentons, dans ce survol, de présenter une structure méconnue : l'algèbre de Lie ARI et son groupe GARI. Puis nous montrons quels progrès elle a déjà permis de réaliser dans l'étude arithmético-algébrique des valeurs zêta multiples et aussi quelles possibilités elle ouvre pour l'exploration du phénomène plus général de /emph{dimorphie numérique}.

Arithmetic diophantine approximation for continued fractions-like maps on the interval

Avraham Bourla (2014)

Acta Arithmetica

We establish arithmetical properties and provide essential bounds for bi-sequences of approximation coefficients associated with the natural extension of maps, leading to continued fraction-like expansions. These maps are realized as the fractional part of Möbius transformations which carry the end points of the unit interval to zero and infinity, extending the classical regular and backwards continued fraction expansions.

Currently displaying 1681 – 1700 of 1964