算法数论Algorithmic number theory

2002-12  

1 edition (2002年9月1日)  

Claus Fieker  

517  

This book constitutes the refereed proceedings of the 5th International Algorithmic Number Theory Symposium, ANTS-V, held in Sydney, Australia, in July 2002.The 34 revised full papers presented together with 5 invited papers have gone through a thorough round of reviewing, selection and revision. The papers are organized in topical sections on number theory, arithmetic geometry, elliptic curves and CM, point counting, cryptography, function fields, discrete logarithms and factoring, Groebner bases, and complexity.

Invited Talks　Gauss Composition and Generalizations　Elliptic Curves-The Crossroads of Theory and Computation　The Weil and Tate Pairings as Building Blocks for Public Key Cryptosystems　Using Elliptic Curves of Rank One towards the Undecidability of Hilbert's Tenth Problem over 　Rings of Algebraic Integers　On p-adic Point Counting Algorithms for Elliptic Curves over Finite FieldsNumber Theory　On Arithmetically Equivalent Number Fields of Small Degree　A Survey of Discriminant Counting　A Higher-Rank Mersenne Problem　An Application of Siegel Modular Functions to Kronecker's Limit Formula　Computational Aspects of NUCOMP　Efficient Computation of Class Numbers of Real Abelian Number Fields 　An Accelerated Buchmann Algorithm for Regulator Computation in Real Quadratic FieldsArithmetic Geometry Some Genus 3 Curves with Many Points　Trinomials ax7 + bx + c and axs + bx + c with Galois Groups of Order 168 and 8 - 168　Computations on Modular Jacobian Surfaces　Integral Points on Punctured Abelian Surfaces　Genus 2 Curves with (3, 3)-Split Jacobian and Large Automorphism Group　Transportable Modular Symbols and the Intersection PairingElliptic Curves and CM　Action of Modular Correspondences around CM Points　Curves Dy2 = x3 - x of Odd Analytic Rank　Comparing Invariants for Class Fields of Imaginary Quadratic Fields .　A Database of Elliptic Curves - First ReportPoint Counting　Isogeny Volcanoes and the SEA Algorithm　Fast Elliptic Curve Point Counting Using Gaussian Normal Basis　An Extension of Kedlaya's Algorithm to Artin-Schreier Curves in Characteristic 2CyptographyFunction FieldsDiscrete Logarithms and FactoringGrobner BasesComplexityAuthor Index

From the reviews: "The book contains 39 articles about computational algebraic number theory, arithmetic geometry and cryptography. a ] The articles in this book reflect the broad interest of the organizing committee and the participants. The emphasis lies on the mathematical theory as well as on computational results. We recommend the book to students and researchers who want to read about current research in number theory and arithmetic geometry and its applications." (R. Carls, Nieuw Archief voor Wiskunde, Vol. 6 (3), 2005)

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