Table of contents for Algorithmic number theory : 6th international symposium, ANTS-VI, Burlington, VT, USA, June 13-18, 2004 : proceedings / Duncan Buell (ed.).


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Invited Talks

Computing Zeta Functions via p-Adic Cohomology ....................  1
   Kiran S. Kedlaya

Using Primitive Subgroups to Do More with Fewer Bits ............... 18
   K. Rubin, A. Silverberg

Elliptic Curves of Large Rank and Small Conductor ........   ....... 42
   Noam D. Elkies, Mark Watkins

Contributed Papers

Binary GCD Like Algorithms for Some Complex Quadratic Rings ....... 57
   Saurabh Agarwal, Gudmund Skovbjerg Frandsen

On the Complexity of Computing Units in a Number Field ............ .  72
   V. Arvind, Piyush P. Kurur

Implementing the Arithmetic of C3,4 Curves ..........................  87
   Abdolali Basiri, Andreas Enge, Jean-Charles Faug&re,
   Nicolas Giirel

Pseudocubes and Primality Testing ................................. 102
   P. Berrizbeitia, S. Miiller, H.C. Williams

Elliptic Curves with a Given Number of Points ....................... 117
   Reinier Broker, Peter Stevenhagen

Rational Divisors in Rational Divisor Classes  ......................... 132
   N. Bruin, E. V. Flynn

Conjectures about Discriminants of Hecke Algebras of Prime Level ...... 140
   Frank Calegari, William A. Stein

Montgomery Scalar Multiplication for Genus 2 Curves ................. 153
   Sylvain Duquesne

Improved Weil and Tate Pairings for Elliptic
and Hyperelliptic Curves ...............    ........................... 169
   Kirsten Eisentriger, Kristin Lauter, Peter L. Montgomery

Elliptic Curves x3 + y3 = k of High Rank ............................ 184
    Noam D. Elkies, Nicholas F. Rogers




Proving the Primality of Very Large Numbers with fastECPP .......... 194
   J. Franke, T. Kleinjung, F. Morain, T. Wirth

A Low-Memory Parallel Version of Matsuo, Chao, and
Tsujii's Algorithm ...............................................   208
   Pierrick Gaudry, Eric Schost

Function Field Sieve in Characteristic Three .......................... 223
   R. Granger, A.J. Holt, D. Page, N.P. Smart, F. Vercauteren

A Comparison of CEILIDH and XTR ...................... 235
   R. Granger, D. Page, M. Stam

Stable Models of Elliptic Curves, Ring Class Fields,
and Complex Multiplication ...................................... .  250
   Jordi Guardia, Eugenia Torres, Montserrat Vela

An Algorithm for Computing Isomorphisms
of Algebraic Function Fields ........................................ 263
   F. Hess

A Method to Solve Cyclotomic Norm Equations f     . f  ............. 272
   Nick Howgrave-Graham, Mike Szydlo

Imaginary Cyclic Quartic Fields with Large Minus Class Numbers ...... 280
   M.J. Jacobson, Jr., H.C. Williams, K. Wooding

Nonic 3-adic Fields ............................................. 293
   John W. Jones, David P. Roberts

Montgomery Addition for Genus Two Curves ........................ 309
   Tanja Lange

Numerical Evaluation at Negative Integers of the Dedekind Zeta
Functions of Totally Real Cubic Number Fields ...................... 318
   Stephane R. Louboutin

Salem Numbers of Trace -2 and Traces of Totally Positive
Algebraic Integers ................................................ 327
   James McKee, Chris Smyth

Low-Dimensional Lattice Basis Reduction Revisited ................... 338
   Phong Q. Nguyen, Damien SteUhl

Computing Order Statistics in the Farey Sequence ................... . 358
   Corina E. Pdtrascu, Mihai Pdtrascu

The Discrete Logarithm in Logarithmic I-Class Groups and Its
Applications in K-theory ................ ............................ 367
   Sebastian Pauli, Florence Soriano-Gafiuk




Point Counting on Genus 3 Non Hyperelliptic Curves .................. 379
   Christophe Ritzenthaler

Algorithmic Aspects of Cubic Function Fields ........................ 395
   R. Scheidler

A Binary Recursive Gcd Algorithm  .........       ......................... 411
   Damien Stehl, Paul Zimmermann

Lagrange Resolvents Constructed from Stark Units .................... 426
   Brett A. Tangedal

Cryptanalysis of a Divisor Class Group Based
Public-Key Cryptosystem .......................................... 442
   Aaram Yun, Jaeheon Kim, Dong Hoon Lee

Author Index ....................................                   451





Library of Congress Subject Headings for this publication: Number theory Congresses