Algebraic Curves over Finite Fields

Develops the theory of algebraic curves over finite fields, their zeta and L-functions and the theory of algebraic geometric Goppa codes.

Carlos Moreno (Author)

9780521459013, Cambridge University Press

Paperback, published 14 October 1993

260 pages
22.9 x 15.2 x 1.5 cm, 0.39 kg

' … a careful and comprehensive guide to some of the most fascinating of plasma processes, a treatment that is both thorough and up-to-date.' The Observatory

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. Amongst 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 Tsfasman–Vladut–Zink 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.

1. Algebraic curves and function fields
2. The Riemann–Roch theorem
3. Zeta functions
4. Applications to exponential sums and zeta functions
5. Applications to coding theory
Bibliography.

Subject Areas: Number theory [PBH]