Algorithmic Arithmetic Geometry And Coding Theory Pdf

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• Obituary and Foreword
• Arithmetic, Geometry, Cryptography and Coding Theory 2009
• Publications

Obituary and Foreword

Research Interests: Arithmetic algebraic geometry: Modular curves, Shimura varieties, moduli spaces, elliptic curves, modular and automorphic forms, zeta functions of varieties over finite fields, computational and algorithmic aspects Number theory: Algebraic number theory, quaternion algebras, quadratic forms, elementary number theory, cryptography, coding theory. Publications: Please note that the versions that appear here may differ from the published version, as some errata have been corrected. The version here is the most updated; the arXiv versions are updated less often. Tables: Hilbert modular forms Totally real number fields of fixed degree and bounded root discriminant Shimura curves of genus at most two Definite Eichler orders with class number at most two. Lattice methods for algebraic modular forms on classical groups with Matthew Greenberg , accepted to "Computations with modular forms". Minimal isospectral and nonisometric 2-orbifolds with Peter Doyle and Benjamin Linowitz , in preparation. Computing power series expansions of modular forms with John Willis , accepted to "Computations with modular forms".

Arithmetic, Geometry, Cryptography and Coding Theory 2009

JavaScript is disabled for your browser. Some features of this site may not work without it. Doctoral thesis. Utgivelsesdato Samlinger Department of Informatics [].

Abelard, P. Gaudry, and P. Spaenlehauer , Improved complexity bounds for counting points on hyperelliptic curves , Foundations of Computational Mathematics , DOI : Leonard, M. Adleman, and.

Algorithmic arithmetic, geometry, and coding theory: 14th International Conference on Arith- metic, Geometry, Cryptography, and Coding Theory, June 3​-7

Publications

Theme: Arithmetic Geometry: Curves and their Jacobians Arithmetic Geometry is the meeting point of algebraic geometry and number theory: that is, the study of geometric objects defined over arithmetic number systems such as the integers and finite fields. The fundamental objects for our applications in both coding theory and cryptology are curves and their Jacobians over finite fields. Not every curve is planar—we may have more variables, and more defining equations—but from an algorithmic point of view, we can always reduce to the plane setting.

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