Arithmetic, Geometry and Coding Theory (AGCT 2003) by Yves Aubry, Gilles Lachaud PDF

By Yves Aubry, Gilles Lachaud

Résumé :
Arithmétique, géométrie et théorie des codes (AGCT 2003)
En mai 2003 se sont tenus au Centre overseas de Rencontres Mathématiques à Marseille (France), deux événements centrés sur l'Arithmétique, l. a. Géométrie et leurs functions à los angeles théorie des Codes ainsi qu'à l. a. Cryptographie : une école Européenne ``Géométrie Algébrique et Théorie de l'Information'' ainsi que los angeles 9ème édition du colloque foreign ``Arithmétique, Géométrie et Théorie des Codes''. Certains des cours et des conférences font l'objet d'un article publié dans ce quantity. Les thèmes abordés furent à los angeles fois théoriques pour certains et tournés vers des functions pour d'autres : variétés abéliennes, corps de fonctions et courbes sur les corps finis, groupes de Galois de pro-p-extensions, fonctions zêta de Dedekind de corps de nombres, semi-groupes numériques, nombres de Waring, complexité bilinéaire de l. a. multiplication dans les corps finis et problèmes de nombre de classes.

Mots clefs : Fonctions zêta, variétés abéliennes, corps de fonctions, courbes sur les corps finis, excursions de corps de fonctions, corps finis, graphes, semi-groupes numériques, polynômes sur les corps finis, cryptographie, courbes hyperelliptiques, représentations p-adiques, excursions de corps de classe, groupe de Galois, issues rationels, fractions maintains, régulateurs, nombre de sessions d'idéaux, complexité bilinéaire, jacobienne hyperelliptiques

In could 2003, occasions were held within the ``Centre foreign de Rencontres Mathématiques'' in Marseille (France), dedicated to mathematics, Geometry and their purposes in Coding thought and Cryptography: an ecu college ``Algebraic Geometry and data Theory'' and the 9-th overseas convention ``Arithmetic, Geometry and Coding Theory''. many of the classes and the meetings are released during this quantity. the themes have been theoretical for a few ones and became in the direction of functions for others: abelian kinds, functionality fields and curves over finite fields, Galois staff of pro-p-extensions, Dedekind zeta features of quantity fields, numerical semigroups, Waring numbers, bilinear complexity of the multiplication in finite fields and sophistication quantity problems.

Key phrases: Zeta features, abelian kinds, capabilities fields, curves over finite fields, towers of functionality fields, finite fields, graphs, numerical semigroups, polynomials over finite fields, cryptography, hyperelliptic curves, p-adic representations, classification box towers, Galois teams, rational issues, endured fractions, regulators, excellent type quantity, bilinear complexity, hyperelliptic jacobians

Class. math. : 14H05, 14G05, 11G20, 20M99, 94B27, 11T06, 11T71, 11R37, 14G10, 14G15, 11R58, 11A55, 11R42, 11Yxx, 12E20, 14H40, 14K05

Table of Contents

* P. Beelen, A. Garcia, and H. Stichtenoth -- On towers of functionality fields over finite fields
* M. Bras-Amorós -- Addition habit of a numerical semigroup
* O. Moreno and F. N. Castro -- at the calculation and estimation of Waring quantity for finite fields
* G. Frey and T. Lange -- Mathematical historical past of Public Key Cryptography
* A. Garcia -- On curves over finite fields
* F. Hajir -- Tame pro-p Galois teams: A survey of modern work
* E. W. Howe, okay. E. Lauter, and J. most sensible -- unnecessary curves of genus 3 and four
* D. Le Brigand -- genuine quadratic extensions of the rational functionality box in attribute two
* S. R. Louboutin -- specific top bounds for the residues at s=1 of the Dedekind zeta services of a few absolutely actual quantity fields
* S. Ballet and R. Rolland -- at the bilindar complexity of the multiplication in finite fields
* Yu. G. Zarhin -- Homomorphisms of abelian forms

Show description

Read or Download Arithmetic, Geometry and Coding Theory (AGCT 2003) PDF

Similar number theory books

New PDF release: The Prime Numbers and Their Distribution (Student

We now have been interested in numbers--and leading numbers--since antiquity. One outstanding new path this century within the learn of primes has been the inflow of rules from chance. The target of this e-book is to supply insights into the leading numbers and to explain how a series so tautly decided can comprise this type of impressive volume of randomness.

Download PDF by Jacques Istas: Mathematical Modeling for the Life Sciences

Offering a variety of mathematical versions which are at present utilized in existence sciences will be considered as a problem, and that's exactly the problem that this e-book takes up. after all this panoramic learn doesn't declare to supply an in depth and exhaustive view of the various interactions among mathematical types and existence sciences.

Read e-book online The Theory of Algebraic Number Fields PDF

This e-book is a translation into English of Hilbert's "Theorie der algebraischen Zahlkrper" most sensible often called the "Zahlbericht", first released in 1897, during which he supplied an elegantly built-in review of the improvement of algebraic quantity concept as much as the top of the 19th century. The Zahlbericht supplied additionally an organization beginning for additional study within the topic.

Additional info for Arithmetic, Geometry and Coding Theory (AGCT 2003)

Sample text

10 this implies t(F ) = ν(F ). Moreover, we have seen that the completely splitting places in the tower F are described by solutions of the functional equation for ϕ(t) := (1−t)/tq and ψ(t) := (tq +t−1)/t. 4 that ´ ` 11 SEMINAIRES & CONGRES TOWERS OF FUNCTION FIELDS 19 essentially only one solution H(t, s) exists, we would be done. , Pω is defined as the zero of x1 − ω) would then be given by H(ω q + ω − 1, ω) = 0. As it is, we cannot apply the proposition directly. However, we can rewrite the defining equation of the tower F .

Math. (to appear). G. G. Vladut – The number of points of an algebraic curve, Func. Anal. 17 (1983), p. 53–54. M. Duursma, B. Poonen & M. L. Mullen, A. Poli & H. ), Lecture Notes in Computer Science, vol. 2948, Springer, 2004, p. 148–153. [9] A. Garcia & H. Stichtenoth – On the asymptotic behaviour of some towers of function fields over finite fields, J. Number Theory 61 (1996), p. 248–273. , Skew pyramids of function fields are asymptotically bad, in Coding Theory, [10] Cryptography and Related Areas (J.

A numerical semigroup Λ is uniquely determined by the binary operation ⊕. Proof. — We will show that Λ is unique by proving that λi is uniquely determined by ⊕ for all i ∈ N0 . 4, i ⊕ j j + λi for all j, i ⊕ j = j + λi for all j with λj c. Therefore, maxj {i ⊕ j − j} exists for all i, is uniquely determined by ⊕ and it is exactly λi . 2. The sequence (νi ) determines a semigroup In this section we prove that any numerical semigroup is uniquely determined by the associated sequence (νi ). We will use the following well-known result on the values νi .

Download PDF sample

Rated 4.82 of 5 – based on 49 votes