Séminaires et Congrès 2005; 216 pp; softcover Number: 11 ISBN10: 2856291759 ISBN13: 9782856291757 List Price: US$59 Member Price: US$47.20 Order Code: SECO/11
 In May 2003, two events were held in the CIRM (MarseilleLuminy) 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. BrasAmorós  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 prop 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
