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

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

This publication presents an obtainable and self-contained creation to the idea of algebraic curves over a finite box, a subject matter that has been of basic significance to arithmetic for a few years and that has crucial purposes in parts akin to finite geometry, quantity thought, 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 easy wisdom of algebra and geometry. The detailed 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 idea of Stöhr and Voloch. The procedure of Hasse and Weil through zeta services is defined, after which cognizance turns to extra complicated effects: a state of the art advent to maximal curves over finite fields is equipped; a finished account is given of the automorphism team of a curve; and a few functions to coding idea and finite geometry are defined. The e-book comprises many examples and routines. it's an vital source for researchers and the correct 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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