Download 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 ebook offers an obtainable and self-contained creation to the idea of algebraic curves over a finite box, an issue that has been of primary value to arithmetic for a few years and that has crucial purposes in components akin to finite geometry, quantity thought, 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 through constructing the overall thought 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 exact homes curve over a finite box may have are then mentioned. The geometrical thought 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 process of Hasse and Weil through zeta services is defined, after which consciousness turns to extra complex effects: a cutting-edge creation to maximal curves over finite fields is supplied; a finished account is given of the automorphism staff of a curve; and a few functions to coding concept and finite geometry are defined. The e-book contains many examples and routines. it truly is an integral source for researchers and the proper textbook for graduate students.

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