Many Rational Points: Coding Theory and Algebraic Geometry by N.E. HurtMany Rational Points: Coding Theory and Algebraic Geometry by N.E. Hurt

Many Rational Points: Coding Theory and Algebraic Geometry

byN.E. Hurt

Paperback | December 8, 2010

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This monograph presents a comprehensive treatment of recent results on algebraic geometry as they apply to coding theory and cryptography, with the goal the study of algebraic curves and varieties with many rational points. They book surveys recent developments on abelian varieties, in particular the classification of abelian surfaces, hyperelliptic curves, modular towers, Kloosterman curves and codes, Shimura curves and modular jacobian surfaces. Applications of abelian varieties to cryptography are presented including a discussion of hyperelliptic curve cryptosystems. The inter-relationship of codes and curves is developed building on Goppa's results on algebraic-geometry cods. The volume provides a source book of examples with relationships to advanced topics regarding Sato-Tate conjectures, Eichler-Selberg trace formula, Katz-Sarnak conjectures and Hecke operators.
Title:Many Rational Points: Coding Theory and Algebraic GeometryFormat:PaperbackDimensions:368 pages, 9.25 × 6.1 × 0 inPublished:December 8, 2010Publisher:Springer NetherlandsLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9048164966

ISBN - 13:9789048164967

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From the reviews:"This book gives a nice overview of background and recent results on curves over finite fields. . The main advantage of this book is that it provides a huge bibliography and takes into account even very recent results which are so far only presented at conferences or in preprints. So it serves well to get an update on recent results for the experienced reader and links to the original results for more details." (Tanja Lange, Zentralblatt MATH, Vol. 1072 (23), 2005)