Many Rational Points

Coding Theory and Algebraic Geometry

By:

N.E. Hurt

Format:

Paperback / softback

Series:

Mathematics and its Applications

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Description

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.

Release date Australia

December 8th, 2010

Author

N.E. Hurt

Audience

Professional & Vocational

Illustrations

XXI, 346 p.

Pages

346

Series

Mathematics and its Applications

Dimensions

155x235x19

ISBN-13

9789048164967

Product ID

8939921

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