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

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

This booklet offers an obtainable and self-contained creation to the idea of algebraic curves over a finite box, a subject matter that has been of primary significance to arithmetic for a few years and that has crucial functions in components similar to finite geometry, quantity concept, 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 via constructing the final idea of curves over any box, highlighting peculiarities happening for optimistic attribute and requiring of the reader in basic terms uncomplicated wisdom of algebra and geometry. The particular homes curve over a finite box could 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 strategy 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 crew of a curve; and a few purposes to coding conception and finite geometry are defined. The booklet comprises many examples and routines. it really is an critical 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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