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)
Discussion of theory and applications of algebraic curves over finite fields with many rational points.
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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