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Algorithmic Number Theory

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

  • Conference proceedings
  • © 2004

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Editors:
  1. Duncan Buell

    1. Department of Computer Science and Engineering, University of South Carolina , Columbia, USA

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

Included in the following conference series:

Conference proceedings info: ANTS 2004.

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Table of contents (33 papers)

  1. Front Matter

    Download chapter PDF

  2. Invited Talks

    1. Computing Zeta Functions via p-Adic Cohomology

      • Kiran S. Kedlaya
      Pages 1-17

    2. Using Primitive Subgroups to Do More with Fewer Bits

      • K. Rubin, A. Silverberg
      Pages 18-41

    3. 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 C 3,4 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. Montgomery Scalar Multiplication for Genus 2 Curves

      • Sylvain Duquesne
      Pages 153-168

    9. Improved Weil and Tate Pairings for Elliptic and Hyperelliptic Curves

      • Kirsten Eisenträger, Kristin Lauter, Peter L. Montgomery
      Pages 169-183

    10. Elliptic Curves x 3 + y 3 = k of High Rank

      • Noam D. Elkies, Nicholas F. Rogers
      Pages 184-193

    11. Proving the Primality of Very Large Numbers with fastECPP

      • J. Franke, T. Kleinjung, F. Morain, T. Wirth
      Pages 194-207

    12. A Low-Memory Parallel Version of Matsuo, Chao, and Tsujii’s Algorithm

      • Pierrick Gaudry, Éric Schost
      Pages 208-222

    13. Function Field Sieve in Characteristic Three

      • R. Granger, A. J. Holt, D. Page, N. P. Smart, F. Vercauteren
      Pages 223-234

    14. A Comparison of CEILIDH and XTR

      • R. Granger, D. Page, M. Stam
      Pages 235-249

    15. Stable Models of Elliptic Curves, Ring Class Fields, and Complex Multiplication

      • Jordi Guàrdia, Eugenia Torres, Montserrat Vela
      Pages 250-262

    16. An Algorithm for Computing Isomorphisms of Algebraic Function Fields

      • F. Hess
      Pages 263-271
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  1. Algorithmic Number Theory

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About this book

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.

Editors and Affiliations

  • Department of Computer Science and Engineering, University of South Carolina , Columbia, USA

    Duncan Buell

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