The Number Of Rational Points On Curves Over Finite Fields
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Rational Points on Curves Over Finite Fields
Author: Harald Niederreiter
language: en
Publisher: Cambridge University Press
Release Date: 2001-06-14
Ever since the seminal work of Goppa on algebraic-geometry codes, rational points on algebraic curves over finite fields have been an important research topic for algebraic geometers and coding theorists. The focus in this application of algebraic geometry to coding theory is on algebraic curves over finite fields with many rational points (relative to the genus). Recently, the authors discovered another important application of such curves, namely to the construction of low-discrepancy sequences. These sequences are needed for numerical methods in areas as diverse as computational physics and mathematical finance. This has given additional impetus to the theory of, and the search for, algebraic curves over finite fields with many rational points. This book aims to sum up the theoretical work on algebraic curves over finite fields with many rational points and to discuss the applications of such curves to algebraic coding theory and the construction of low-discrepancy sequences.
Rational Points on Curves Over Finite Fields
In 1985 Jean-Pierre Serre gave a series of lectures at Harvard University on the number of points of curves over finite fields. Based on notes taken at that time by F. Q. Gouvea, the present revised and completed documents provides an insightful introduction to this beautiful topic and to most of the ideas that have been developed in this area during the last 30 years.
Rational Points on Curves Over Finite Fields
Discussion of theory and applications of algebraic curves over finite fields with many rational points.