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 t
Rational points on curves over finite fields
β Scribed by Jean-Pierre Serre; Christophe Ritzenthaler (editor); Elisa Lorenzo GarcΓa (editor); RenΓ© Schoof (editor); Alp Bassa (editor)
- Year
- 2020
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This volume presents the results of the AMS-IMS-SIAM Joint Summer Research Conference held at the University of Washington (Seattle). The talks were devoted to various aspects of the theory of algebraic curves over finite fields and its numerous applications. The three basic themes are the following
In this tract, Professor Moreno develops the theory of algebraic curves over finite fields, their zeta and L-functions, and, for the first time, the theory of algebraic geometric Goppa codes on algebraic curves. Among the applications considered are: the problem of counting the number of solutions o
<p>This book provides an accessible and self-contained introduction to the theory of algebraic curves over a finite field, a subject that has been of fundamental importance to mathematics for many years and that has essential applications in areas such as finite geometry, number theory, error-correc