Rational Points on Curves Over Finite Fields: Theory and Applications

ISBN-13: 9780521665438 / Angielski / Miękka / 2001 / 256 str.

Harald Niederreiter; Chaoping Xing; J. W. S. Cassels

Opis

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.

Recenzje

'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.

Spis treści

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.