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New PDF release: Arithmetic, Geometry and Coding Theory (AGCT 2003)

By Yves Aubry, Gilles Lachaud

ISBN-10: 2856291759

ISBN-13: 9782856291757

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, los angeles Géométrie et leurs purposes à l. a. théorie des Codes ainsi qu'à los angeles Cryptographie : une école Européenne ``Géométrie Algébrique et Théorie de l'Information'' ainsi que l. a. 9ème édition du colloque overseas ``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 l. a. 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 keeps, régulateurs, nombre de sessions d'idéaux, complexité bilinéaire, jacobienne hyperelliptiques

Abstract:
In may perhaps 2003, occasions were held within the ``Centre foreign de Rencontres Mathématiques'' in Marseille (France), dedicated to mathematics, Geometry and their functions in Coding thought and Cryptography: an eu university ``Algebraic Geometry and knowledge Theory'' and the 9-th overseas convention ``Arithmetic, Geometry and Coding Theory''. the various classes and the meetings are released during this quantity. the themes have been theoretical for a few ones and grew to become in the direction of functions for others: abelian types, functionality fields and curves over finite fields, Galois crew of pro-p-extensions, Dedekind zeta services of quantity fields, numerical semigroups, Waring numbers, bilinear complexity of the multiplication in finite fields and sophistication quantity problems.

Key phrases: Zeta capabilities, abelian types, 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, type box towers, Galois teams, rational issues, persevered fractions, regulators, perfect classification 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 heritage of Public Key Cryptography
* A. Garcia -- On curves over finite fields
* F. Hajir -- Tame pro-p Galois teams: A survey of contemporary work
* E. W. Howe, okay. E. Lauter, and J. most sensible -- unnecessary curves of genus 3 and four
* D. Le Brigand -- actual 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 completely genuine quantity fields
* S. Ballet and R. Rolland -- at the bilindar complexity of the multiplication in finite fields
* Yu. G. Zarhin -- Homomorphisms of abelian types

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

Sample text

Exponential sums, solutions of polynomial equations. c S´ eminaires et Congr` es 11, SMF 2005 O. N. CASTRO 30 Let |N | be the number of common zeros to the r polynomials. Introduce r auxiliary variables Y1 , . . , Yr . q r |N | = (Y1 F1 (X1 , . . ,Xn )∈Fq = (Yr Fr (X1 , . . , Xn )) Y1 ∈Fq Yr ∈Fq (Y1 F1 (X) + · · · + Yr Fr (X)). X Y We define L as follows (1) L = min r k=1 n j=1 Nk i=1 where the minimum is taken over all tijk ’s (0 conditions σ(tijk )/(p − 1) − rf, tijk q − 1), satisfying the following t111 + t221 + · · · + t1N1 1 ≡ 0 mod q − 1, t112 + t222 + · · · + t2N2 2 ≡ 0 mod q − 1, ..

Now we return to a tower F over Fq recursively defined by a polynomial f (X, Y ) ∈ Fq [X, Y ]. The function field Fn can be described as Fq (x1 , x2 , . . , xn ) with the relations f (xi , xi+1 ) = 0, for 1 i n − 1. An Fq -rational place P of the function field Fn therefore gives rise to a path of length n − 1 in the graph Γ(f, Fq ). The corresponding sequence of visited vertices is x1 (P ), . . , xn (P ). The number of paths of length n − 1 in the graph therefore gives some information on the number of Fq rational places of the function field Fn .

1041, Herman, Paris, 1948. [17] J. D. Thesis, Universit¨ at Essen, Essen, 2002. [18] T. Zink – Degeneration of Shimura surfaces and a problem in coding theory, in Fundamentals of Computation Theory, Lecture Notes in Computer Science, vol. 199, Springer, Berlin, 1985, p. 503–511. P. dk A. br H. edu ´ ` 11 SEMINAIRES & CONGRES S´ eminaires & Congr` es 11, 2005, p. 21–28 ADDITION BEHAVIOR OF A NUMERICAL SEMIGROUP by Maria Bras-Amor´os Abstract. — In this work we study some objects describing the addition behavior of a numerical semigroup and we prove that they uniquely determine the numerical semigroup.

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


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