Algebraic Curves over a Finite Field (Princeton Series in by J. W.P. Hirschfeld,G. Korchmáros,F. Torres

By J. W.P. Hirschfeld,G. Korchmáros,F. Torres

This publication presents an obtainable and self-contained advent to the idea of algebraic curves over a finite box, a subject matter that has been of primary significance to arithmetic for a few years and that has crucial purposes in components akin to finite geometry, quantity conception, error-correcting codes, and cryptology. in contrast to different books, this one emphasizes the algebraic geometry instead of the functionality box method of algebraic curves.

The authors commence by way of constructing the final thought of curves over any box, highlighting peculiarities taking place for optimistic attribute and requiring of the reader in basic terms simple wisdom of algebra and geometry. The particular homes curve over a finite box may have are then mentioned. The geometrical idea of linear sequence is used to discover estimates for the variety of rational issues on a curve, following the idea of Stöhr and Voloch. The strategy of Hasse and Weil through zeta capabilities is defined, after which recognition turns to extra complicated effects: a cutting-edge creation to maximal curves over finite fields is equipped; a complete account is given of the automorphism workforce of a curve; and a few purposes to coding idea and finite geometry are defined. The e-book comprises many examples and workouts. it truly is an integral source for researchers and the suitable textbook for graduate students.

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