By J. W.P. Hirschfeld,G. Korchmáros,F. Torres
This e-book offers an obtainable and self-contained creation to the idea of algebraic curves over a finite box, a subject matter that has been of basic value to arithmetic for a few years and that has crucial purposes in components similar to finite geometry, quantity idea, error-correcting codes, and cryptology. not like different books, this one emphasizes the algebraic geometry instead of the functionality box method of algebraic curves.
The authors commence by means of constructing the overall idea of curves over any box, highlighting peculiarities happening for optimistic attribute and requiring of the reader in basic terms simple wisdom of algebra and geometry. The specific homes curve over a finite box may have are then mentioned. The geometrical conception of linear sequence is used to discover estimates for the variety of rational issues on a curve, following the speculation of Stöhr and Voloch. The technique of Hasse and Weil through zeta features is defined, after which recognition turns to extra complex effects: a cutting-edge creation to maximal curves over finite fields is supplied; a entire account is given of the automorphism team of a curve; and a few purposes to coding thought and finite geometry are defined. The e-book comprises many examples and workouts. it's an vital source for researchers and the best textbook for graduate students.
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Additional info for Algebraic Curves over a Finite Field (Princeton Series in Applied Mathematics)
Algebraic Curves over a Finite Field (Princeton Series in Applied Mathematics) by J. W.P. Hirschfeld,G. Korchmáros,F. Torres