Algebraic Curves over Finite Fields (Cambridge Tracts in Mathematics, Series Number 97)

Moreno, Carlos

ISBN 10: 052145901X / ISBN 13: 9780521459013

Published by Cambridge University Press, 1994

About this Item

Seller Inventory # 17X97_86_052145901X

Bibliographic Details

• Title: Algebraic Curves over Finite Fields (Cambridge Tracts in Mathematics, Series Number 97)
• Publisher: Cambridge University Press
• Publication Date: 1994
• Language: English
• ISBN 10: 052145901X
• ISBN 13: 9780521459013
• Binding: Soft cover
• Condition: new

About this title

Synopsis

In this tract, Professor Moreno develops the theory of algebraic curves over finite fields, their zeta and L-functions, and, for the first time, the theory of algebraic geometric Goppa codes on algebraic curves. Among the applications considered are: the problem of counting the number of solutions of equations over finite fields; Bombieri's proof of the Reimann hypothesis for function fields, with consequences for the estimation of exponential sums in one variable; Goppa's theory of error-correcting codes constructed from linear systems on algebraic curves; there is also a new proof of the TsfasmanSHVladutSHZink theorem. The prerequisites needed to follow this book are few, and it can be used for graduate courses for mathematics students. Electrical engineers who need to understand the modern developments in the theory of error-correcting codes will also benefit from studying this work.

Book Description

The theory of algebraic curves over finite fields, their zeta and L-functions, and, for the first time, the theory of algebraic geometric Goppa codes on algebraic curves are developed in this text. Electrical engineers as well as mathematics students will find the material of interest.