Rational Points on Curves over Finite Fields: Theory and Applications

by Harald Niederreiter, Chaoping Xing

Overview

Rational points on algebraic curves over finite fields is a key topic for algebraic geometers and coding theorists. Here, the authors relate an important application of such curves, namely, to the construction of low-discrepancy sequences, needed for numerical methods in diverse areas. They sum up the theoretical work on algebraic curves over finite fields with many rational points and discuss the applications of such curves to algebraic coding theory and the construction of low-discrepancy sequences.

Product Details

ISBN-13:	9780521665438
Publisher:	Cambridge University Press
Publication date:	06/14/2001
Series:	London Mathematical Society Lecture Note Series , #285
Pages:	256
Product dimensions:	6.06(w) x 8.98(h) x 0.63(d)

Table of Contents

1. Background on function fields; 2. Class field theory; 3. Explicit function fields; 4. Function fields with many rational places; 5. Asymptotic results; 6. Applications to algebraic coding theory; 7. Applications to cryptography; 8. Applications to low-discrepancy sequences.

Editorial Reviews

'… the book under review develops many techniques that are not covered in the existing texts. I highly recommend it.' Steven D. Galbraith, Royal Holloway, University of London

'Because of the carefully selected contents and lucid style, the book can be warmly recommended to mathematicians interested in the above-mentioned topics or in algebraic curves over finite fields with many rational points.' EMS

'The book is very clearly written. It is warmly recommended to anyone who is interested in nice mathematical theories and/or in the recent applications.' Acta. Sci. Math.

From the Publisher

Ever since Hasse and Weil's work in the 1930s and 1940s, algebraic curves over finite fields and their function fields have attracted both number theorists and specialists in geometry. Niederreiter and Xing, both at the National U. of Singapore, present classic field theory, recent research using the methods of algebraic geometry, and applications in algebraic coding theory and cryptography, among other topics. Includes tables of upper and lower bounds, and 188 references. Annotation c. Book News, Inc., Portland, OR (booknews.com)