Rational Points on Curves over Finite Fields: Theory and Applications

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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.

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Editorial Reviews

From the Publisher
'… 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 Critics
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)
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Product Details

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.

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