Algorithmic Number Theory

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 Fields.- Algebraic 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 Polynomial.- Analytic 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 Pseudocubes.- Lattices.- Practical Lattice Basis Sampling Reduction.- LLL on the Average.- On the Randomness of Bits Generated by Sufficiently Smooth Functions.- Curves and Varieties over Fields of Characteristic Zero.- Computing a Lower Bound for the Canonical Height on Elliptic Curves over ?.- Points of Low Height on Elliptic Curves and Surfaces I: Elliptic Surfaces over with Small d.- Shimura Curves for Level-3 Subgroups of the (2,3,7) Triangle Group, and Some Other Examples.- The Asymptotics of Points of Bounded Height on Diagonal Cubic and Quartic Threefolds.- Testing Equivalence of Ternary Cubics.- Classification of Genus 3 Curves in Special Strata of the Moduli Space.- Heegner Point Computations Via Numerical p-Adic Integration.- Symmetric Powers of Elliptic Curve L-Functions.-Determined Sequences, Continued Fractions, and Hyperelliptic Curves.- Computing CM Points on Shimura Curves Arising from Cocompact Arithmetic Triangle Groups.- Arithmetic of Generalized Jacobians.- Hidden Pairings and Trapdoor DDH Groups.- Constructing Pairing-Friendly Elliptic Curves with Embedding Degree 10.- Fast Bilinear Maps from the Tate-Lichtenbaum Pairing on Hyperelliptic Curves.- High Security Pairing-Based Cryptography Revisited.- Efficiently Computable Endomorphisms for Hyperelliptic Curves.- Construction of Rational Points on Elliptic Curves over Finite Fields.- 20 Years of ECM.- Discrete Logarithms.- An Index Calculus Algorithm for Plane Curves of Small Degree.- Signature Calculus and Discrete Logarithm Problems.- Spectral Analysis of Pollard Rho Collisions.- Hard Instances of the Constrained Discrete Logarithm Problem.