7th Algorithmic Number Theory Symposium, 23 - 28 July 2006 Proceedings

The refereed Proceedings of ANTS VII are published in the Springer series Lecture Notes in Computer Science Volume 4076 and were handed to the participants when they check in. They are also available electronically. The articles are organized into the chapters Invited Talks, 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. On this page you find slides of talks, source code of programs, errata, and other additional material. Selfridge Prize in Computational Number Theory [Communicated by Hugh Williams] In honour of the many contributions of John Selfridge to mathematics, the Number Theory Foundation has established a prize to be awarded to those individuals who have authored the best paper accepted for presentation at ANTS. The prize, called the Selfridge Prize, will normally be awarded every two years in an even numbered year. The prize winner(s) receive a cash award and a certificate. The successful paper will be selected by the ANTS Program Committee. Werner Bley and Robert Boltje were awarded the Selfridge Prize in Computational Number Theory for their paper Computation of locally free class groups. Invited Talks Computing Pro-P Galois Groups Nigel Boston and Harris Nover Talk The Elliptic Curve Database John Cremona Database, Errata, Talk On the Computation of the Coefficients of a Modular Form Bas Edixhoven Talk Cohen-Lenstra heuristics of quadratic number fields Etienne Fouvry and Jürgen Klüners (q-Hypergeometric Series and Modular Forms) Don Zagier Algebraic Number Theory An algorithm for computing p-class groups of abelian number fields Miho Aoki and Takashi Fukuda Computation of locally free class groups Werner Bley and Robert Boltje Numerical Results on Class Groups of Imaginary Quadratic Fields M.J. Jacobson, S. Ramachandran, H.C. Williams Supplementary Tables Cyclic polynomials arising from Kummer theory of norm algebraic tori Masanari Kida The totally real primitive number fields of discriminant at most 109 Gunter Malle A Modular Method for Computing the Splitting Field of a Polynomial Guénaël Renault and Kazuhiro Yokoyama Analytic and Elementary Number Theory The Density of Sums of Three Cubes Jean-Marc Deshouillers, Francois Hennecart, Bernard Landreau The Mertens Conjecture Revisited Tadej Kotnik and And Herman te Riele Talk, Errata: page 158, line -7, "by Theorem 1" should read: "by Theorem 2". Fast Bounds on the Distribution of Smooth Numbers Scott T. Parsell and Jonathan P. Sorenson Use of Extended Euclidean Algorithm in Solving a System of Linear Diophantine Equations with Bounded Variables Parthasarathy Ramachandran The Pseudosquares Prime Sieve Jonathan P. Sorenson Doubly-Focused Enumeration of Pseudosquares and Pseudocubes Kjell Wooding and H. C. Williams Lattices Practical Lattice Basis Sampling Reduction Johannes Buchmann and Christoph Ludwig LLL on the average Phong Q. Nguyen and Damien Stehlé On the Randomness of Bits Produced by Sufficiently Regular Functions Damien Stehlé Curves and Varieties over Fields of Characteristic Zero Computing a Lower Bound for the Canonical Height on Elliptic Curves over Q John Cremona and Samir Siksek Points of Low Height on Elliptic Curves and Surfaces I: Elliptic Surfaces over P1 with small d Noam D. Elkies Shimura Curves for Level-3 Subgroups of the (2, 3, 7) Triangle Group and Some Other Examples Noam D. Elkies The Asymptotics of Points of Bounded Height on Diagonal Cubic and Quartic Threefolds Andreas-Stephan Elsenhans and Joerg Jahnel Talk, C-Source for hashing package, C-Source for solving x4 + 2 y4 = z4 + 4 w4 Testing Equivalence of Ternary Cubics Tom Fisher Classification of Genus 3 Curves in Special Strata of the Moduli Space Martine Girard, David Kohel Heegner point computations via numerical p-adic integration Matthew Greenberg Symmetric Powers of Elliptic Curve L-Functions Phil Martin and Mark Watkins Determined sequences, continued fractions, and hyperelliptic curves Alfred J. van der Poorten Computing CM Points on Shimura Curves Arising from Cocompact Arithmetic Triangle Groups John Voight Curves over Finite Fields and Applications Arithmetic of Generalized Jacobians Isabelle Dechene Hidden Pairings and Trapdoor DDH Groups Alexander W. Dent and Steven D. Galbraith Talk (PDF, PPT) Constructing Pairing-Friendly Elliptic Curves with Embedding Degree 10 David Freeman Fast bilinear maps from the Tate-Lichtenbaum pairing on hyperelliptic curves Gerhard Frey and Tanja Lange High Security Pairing-Based Cryptography Revisited R. Granger, D. Page, and N.P. Smart Efficiently Computable Endomorphisms for Hyperelliptic Curves David R. Kohel, Benjamin A. Smith Finding Points on Elliptic Curves in Deterministic Polynomial Time Andrew Shallue and Christiaan van de Woestijne Implementation for odd characteristic: ellpoint.magma, implementation.magma 20 years of ECM Paul Zimmermann and Bruce Dodson Discrete Logarithms Index Calculus with Double Large Prime Variation in Class Groups of Plane Curves of Small Degree Claus Diem The density of sums of three cubes Jean-Marc DESHOUILLERS, François HENNECART, Bernard LANDREAU Hard Instances of Constrained Discrete Logarithm Problem Ilya Mironov, Anton Mityagin, Kobbi Nissim Corrected Article, Talk (PDF, PPT) Spectral Analysis of Pollard Rho Collisions Stephen D. Miller and Ramarathnam Venkatesan Signature Calculus and Discrete Logarithm Problems Ming-Deh Huang and Wayne Raskind Program Committee Karim Belabas, Universite Bordeaux 1 Johannes Buchmann, Universität Darmstadt John Cannon, University of Sydney Gerhard Frey, Universität Duisburg-Essen Istvan Gaal, University of Debrecen Francois Morain, Ecole Polytechnique Ken Nakamula, Tokyo Metropolitan University Enric Nart, Universitat Autonoma de Barcelona Takakazu Satoh, Tokyo Institute of Technology Peter Stevenhagen, Universiteit Leiden Fernando Villegas, University of Texas Hugh Williams, University of Calgary