Algorithmic Number Theory

6th International Symposium, ANTS-VI, Burlington, VT, USA, June 13-18, 2004, Proceedings

  • Duncan Buell
Conference proceedings ANTS 2004

DOI: 10.1007/b98210

Part of the Lecture Notes in Computer Science book series (LNCS, volume 3076)

Table of contents (33 papers)

  1. Front Matter
  2. Invited Talks

    1. Using Primitive Subgroups to Do More with Fewer Bits
      K. Rubin, A. Silverberg
      Pages 18-41
    2. Elliptic Curves of Large Rank and Small Conductor
      Noam D. Elkies, Mark Watkins
      Pages 42-56
  3. Contributed Papers

    1. Binary GCD Like Algorithms for Some Complex Quadratic Rings
      Saurabh Agarwal, Gudmund Skovbjerg Frandsen
      Pages 57-71
    2. On the Complexity of Computing Units in a Number Field
      V. Arvind, Piyush P. Kurur
      Pages 72-86
    3. Implementing the Arithmetic of C3,4 Curves
      Abdolali Basiri, Andreas Enge, Jean-Charles Faugère, Nicolas Gürel
      Pages 87-101
    4. Pseudocubes and Primality Testing
      P. Berrizbeitia, S. Müller, H. C. Williams
      Pages 102-116
    5. Elliptic Curves with a Given Number of Points
      Reinier Bröker, Peter Stevenhagen
      Pages 117-131
    6. Rational Divisors in Rational Divisor Classes
      N. Bruin, E. V. Flynn
      Pages 132-139
    7. Conjectures about Discriminants of Hecke Algebras of Prime Level
      Frank Calegari, William A. Stein
      Pages 140-152
    8. Improved Weil and Tate Pairings for Elliptic and Hyperelliptic Curves
      Kirsten Eisenträger, Kristin Lauter, Peter L. Montgomery
      Pages 169-183
    9. Elliptic Curves x3 + y3 = k of High Rank
      Noam D. Elkies, Nicholas F. Rogers
      Pages 184-193
    10. Proving the Primality of Very Large Numbers with fastECPP
      J. Franke, T. Kleinjung, F. Morain, T. Wirth
      Pages 194-207
    11. Function Field Sieve in Characteristic Three
      R. Granger, A. J. Holt, D. Page, N. P. Smart, F. Vercauteren
      Pages 223-234
    12. A Comparison of CEILIDH and XTR
      R. Granger, D. Page, M. Stam
      Pages 235-249
    13. Stable Models of Elliptic Curves, Ring Class Fields, and Complex Multiplication
      Jordi Guàrdia, Eugenia Torres, Montserrat Vela
      Pages 250-262

About these proceedings


The sixth Algorithmic Number Theory Symposium was held at the University of Vermont, in Burlington, from 13–18 June 2004. The organization was a joint e?ort of number theorists from around the world. There were four invited talks at ANTS VI, by Dan Bernstein of the Univ- sity of Illinois at Chicago, Kiran Kedlaya of MIT, Alice Silverberg of Ohio State University, and Mark Watkins of Pennsylvania State University. Thirty cont- buted talks were presented, and a poster session was held. This volume contains the written versions of the contributed talks and three of the four invited talks. (Not included is the talk by Dan Bernstein.) ANTS in Burlington is the sixth in a series that began with ANTS I in 1994 at Cornell University, Ithaca, New York, USA and continued at Universit´eB- deaux I, Bordeaux, France (1996), Reed College, Portland, Oregon, USA (1998), the University of Leiden, Leiden, The Netherlands (2000), and the University of Sydney, Sydney, Australia (2002). The proceedings have been published as volumes 877, 1122, 1423, 1838, and 2369 of Springer-Verlag’s Lecture Notes in Computer Science series. The organizers of the 2004 ANTS conference express their special gratitude and thanks to John Cannon and Joe Buhler for invaluable behind-the-scenes advice.


Farey sequence Prime algebraic geometry algebraic number fields algebraic number theory algorithmic number theory algorithms complexity computational number theory elliptic curve computations factoring finite field computations number theory statistics zeta functions

Editors and affiliations

  • Duncan Buell
    • 1
  1. 1.Department of Computer Science and EngineeringUniversity of South Carolina ColumbiaUSA

Bibliographic information

  • Copyright Information Springer-Verlag Berlin Heidelberg 2004
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-22156-2
  • Online ISBN 978-3-540-24847-7
  • Series Print ISSN 0302-9743
  • Series Online ISSN 1611-3349