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

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

This e-book offers an obtainable and self-contained advent to the idea of algebraic curves over a finite box, a subject matter that has been of primary value to arithmetic for a few years and that has crucial purposes in parts similar to finite geometry, quantity conception, 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 through constructing the overall idea of curves over any box, highlighting peculiarities taking place for optimistic attribute and requiring of the reader simply uncomplicated wisdom of algebra and geometry. The certain houses 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 method of Hasse and Weil through zeta features is defined, after which recognition turns to extra complex effects: a state of the art creation to maximal curves over finite fields is equipped; a finished account is given of the automorphism team of a curve; and a few purposes to coding concept and finite geometry are defined. The ebook comprises many examples and workouts. it truly is an critical source for researchers and the fitting textbook for graduate students.

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

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