Rational Points on Curves over Finite Fields: Theory and Applications - Brossura

Niederreiter, Harald

Brossura

ISBN 10: 0521665434 ISBN 13: 9780521665438

Casa editrice: Cambridge University Press, 1997

Riassunto

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.

Su questo libro

Recensione:

'... 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.

Descrizione del libro:

This book gives a summary of the theory and discusses the applications of algebraic curves over finite fields with many rational points. The bulk of the material in this book is of very recent origin and has not been systematically treated in any other works.

Su questa edizione

• Editore: Cambridge University Press
• Data di pubblicazione: 1997
• ISBN 10: 0521665434
• ISBN 13: 9780521665438
• Rilegatura: Copertina flessibile
• Numero di pagine: 256