Algebraic Curves over a Finite Field (Princeton Series in Applied Mathematics): 20 - Image 1

£115.00

Princeton University Press Algebraic Curves over a Finite Field (Princeton Series in Applied Mathematics): 20

Name: Algebraic Curves over a Finite Field (Princeton Series in Applied Mathematics): 20
Brand: Princeton University Press
Price: 115.0 GBP
Availability: InStock

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Description

This book provides an accessible and self-contained introduction to the theory of algebraic curves over a finite field, a subject that has been of fundamental importance to mathematics for many years and that has essential applications in areas such as finite geometry, number theory, error-correcting codes, and cryptology. Unlike other books, this one emphasizes the algebraic geometry rather than the function field approach to algebraic curves. The authors begin by developing the general theory of curves over any field, highlighting peculiarities occurring for positive characteristic and requiring of the reader only basic knowledge of algebra and geometry. The special properties that a curve over a finite field can have are then discussed. The geometrical theory of linear series is used to find estimates for the number of rational points on a curve, following the theory of Stöhr and Voloch. The approach of Hasse and Weil via zeta functions is explained, and then attention turns to more advanced results: a state-of-the-art introduction to maximal curves over finite fields is provided; a comprehensive account is given of the automorphism group of a curve; and some applications to coding theory and finite geometry are described. The book includes many examples and exercises. It is an indispensable resource for researchers and the ideal textbook for graduate students.

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Product Specifications

Brand: Princeton University Press
Format: hardcover
ASIN: 0691096791
Category: Books > Subjects > Science, Nature & Maths > Earth Sciences > Education
Domain: Amazon UK
Release Date: 01 May 2008
Listed Since: 06 February 2007

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Princeton University Press Algebraic Curves over a Finite Field (Princeton Series in Applied Mathematics): 20

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