Algorithmic Number Theory

Inhaltsverzeichnis

• 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.