算法数论Algorithmic number theory

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.

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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 Fields
Number 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 Fields
Arithmetic 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 Pairing
Elliptic 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 Report
Point 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 2
Cyptography
Function Fields
Discrete Logarithms and Factoring
Grobner Bases
Complexity
Author Index