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

This e-book presents an obtainable and self-contained creation to the idea of algebraic curves over a finite box, an issue that has been of primary significance to arithmetic for a few years and that has crucial purposes in parts corresponding to finite geometry, quantity idea, 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 start by way of constructing the overall concept of curves over any box, highlighting peculiarities happening for optimistic attribute and requiring of the reader basically uncomplicated wisdom of algebra and geometry. The distinctive homes curve over a finite box could 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 process of Hasse and Weil through zeta services is defined, after which recognition turns to extra complicated effects: a state of the art creation to maximal curves over finite fields is supplied; a accomplished account is given of the automorphism staff of a curve; and a few purposes to coding idea and finite geometry are defined. The e-book comprises many examples and routines. it truly is an crucial source for researchers and the precise 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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