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Arithmetic, Geometry and Coding Theory (AGCT 2003)
Edited by: Yves Aubry and Gilles Lachaud, Institut de Mathématiques de Luminy, Marseille, France
A publication of the Société Mathématique de France.
Séminaires et Congrès
2005; 216 pp; softcover
Number: 11
ISBN-10: 2-85629-175-9
ISBN-13: 978-2-85629-175-7
List Price: US$59
Member Price: US$47.20
Order Code: SECO/11
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In May 2003, two events were held in the CIRM (Marseille-Luminy) devoted to arithmetic, geometry and their applications in coding theory and cryptography: a European school "Algebraic Geometry and Information Theory" and the 9th international conference "Arithmetic, Geometry and Coding Theory". Some of the courses of the conferences are published in this volume. Topics covered include: Abelian varieties, function fields and curves over finite fields, Galois group of pro-\(p\)-extensions, Dedekind zeta functions of number fields, numerical semigroups, Waring numbers, bilinear complexity of the multiplication in finite fields and class number problems.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.

Table of Contents

  • P. Beelen, A. Garcia, and H. Stichtenoth -- On towers of function fields over finite fields
  • M. Bras-Amorós -- Addition behavior of a numerical semigroup
  • O. Moreno and F. N. Castro -- On the calculation and estimation of Waring number for finite fields
  • G. Frey and T. Lange -- Mathematical background of Public Key Cryptography
  • A. Garcia -- On curves over finite fields
  • F. Hajir -- Tame pro-p Galois groups: A survey of recent work
  • E. W. Howe, K. E. Lauter, and J. Top -- Pointless curves of genus three and four
  • D. Le Brigand -- Real quadratic extensions of the rational function field in characteristic two
  • S. R. Louboutin -- Explicit upper bounds for the residues at \(s=1\) of the Dedekind zeta functions of some totally real number fields
  • S. Ballet and R. Rolland -- On the bilindar complexity of the multiplication in finite fields
  • Yu. G. Zarhin -- Homomorphisms of abelian varieties
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