算法數(shù)論/Algorithmic number theory

內(nèi)容概要

This book constitutes the refereed proceedings of the 7th International Algorithmic Number Theory Symposium, ANTS 2006, held in Berlin, Germany in July 2006.　　The 37 revised full papers presented together with 4 invited papers were carefully reviewed and selected for inclusion in the book. The papers are organized in topical sections on algebraic number theory, analytic and elementary number theory, lattices, curves and varieties over fields of characteristic zero, curves over finite fields and applications, and discrete logarithms.

書籍目錄

Invited Talks  Computing Pro-P Galois Groups  The Elliptic Curve Database for Conductors to 130000  On the Computation of the Coefficients of a Modular Form  Cohen-Lenstra Heuristics of Quadratic Number FieldsAlgebraic Number Theory  An Algorithm for Computing p-Class Groups of Abelian Number Fields  Computation of Locally Free Class Groups  Numerical Results on Class Groups of Imaginary Quadratic Fields  Cyclic Polynomials Arising from Kummer Theory of Norm Algebraic Tori  The Totally Real Primitive Number Fields of Discriminant at Most 109  A Modular Method for Computing the Splitting Field of a PolynomialAnalytic and Elementary Number Theory  On the Density of Sums of Three Cubes  The Mertens Conjecture Revisited  Fast Bounds on the Distribution of Smooth Numbers  Use of Extended Euclidean Algorithm in Solving a System of Linear Diophantine Equations with Bounded Variables  The Pseudosquares Prime Sieve  Doubly-Focused Enumeration of Pseudosquares and PseudocubesLattices  Practical Lattice Basis Sampling Reduction  LLL on the Average  On the Randomness of Bits Generated by Sufficiently Smooth FhnctionsCurves and Varieties over Fields of Characteristic Zero  Computing a Lower Bound for the Canonical Height on Elliptic Curves over Q  Points of Low Height on Elliptic Curves and Surfaces I: Elliptic Surfaces over 171 with Small d  Shimura Curves for Level-3 Subgroups of the (2, 3, 7) Triangle Group and Some Other Examples ……Curves over Finite Fields and ApplicationsDiscrete Lograithms Auhtor Index

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