Algorithmic Number Theory

1. Front Matter

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2. Counting rational points on curves and abelian varieties over finite fields

   • Leonard M. Adleman, Ming-Deh A. Huang

   Pages 1-16

3. Computing cubic fields in quasi-linear time

   • K. Belabas

   Pages 17-25

4. Fast ideal arithmetic via lazy localization

   • Daniel J. Bernstein

   Pages 27-34

5. A comparative study of algorithms for computing continued fractions of algebraic numbers

   • Richard P. Brent, Alfred J. van der Poorten, Herman J. J. te Riele

   Pages 35-47

6. Computing ray class groups, conductors and discriminants

   • H. Cohen, F. Diaz y Diaz, M. Olivier

   Pages 49-57

7. Computing l-isogenies using the p-torsion

   • Jean-Marc Couveignes

   Pages 59-65

8. On computing Hilbert class fields of prime degree

   • M. Daberkow, M. E. Pohst

   Pages 67-74

9. On the reduction of composed relations from the number field sieve

   • Thomas F. Denny, Volker Müller

   Pages 75-90

10. Checking the \(\mathfrak{p}\)-adic stark conjecture when \(\mathfrak{p}\)is archimedean

    • David S. Dummit, David R. Hayes

    Pages 91-97

11. A multiple polynomial general number field sieve

    • Marije Elkenbracht-Huizing

    Pages 99-114

12. Construction of high-rank elliptic curves over ℚ and ℚ(t) with non-trivial 2-torsion

    • Stéfane Fermigier

    Pages 115-120

13. The height on an abelian variety

    • Bríd ní Fhlathúin

    Pages 121-131

14. On lattices over number fields

    • C. Fieker, M. E. Pohst

    Pages 133-139

15. Minimum discriminants of primitive sextic fields

    • David Ford

    Pages 141-143

16. A new algorithm and refined bounds for extended gcd computation

    • David Ford, George Havas

    Pages 145-150

17. Application of thue equations to computing power integral bases in algebraic number fields

    • István Gaál

    Pages 151-155

18. Computing S-integral points on elliptic curves

    • Josef Gebel, Attila Pethő, Horst G. Zimmer

    Pages 157-171

19. Probabilistic computation of the Smith normal form of a sparse integer matrix

    • Mark Giesbrecht

    Pages 173-186

20. Ray class field constructions of curves over finite fields with many rational points

    • Kristin Lauter

    Pages 187-195

This book constitutes the refereed post-conference proceedings of the Second International Algorithmic Number Theory Symposium, ANTS-II, held in Talence, France in May 1996.
The 35 revised full papers included in the book were selected from a variety of submissions. They cover a broad spectrum of topics and report state-of-the-art research results in computational number theory and complexity theory. Among the issues addressed are number fields computation, Abelian varieties, factoring algorithms, finite fields, elliptic curves, algorithm complexity, lattice theory, and coding.

• Algorithmische Zahlentheorie
• Algorithms
• Computational Number Theory
• Constructive Mathematics
• Komplexitätstheorie
• Numbertheoretical Algorithms
• Zahlentheoretische Algorithmen
• algorithm
• complexity
• complexity theory
• finite field
• number theory
• algorithm analysis and problem complexity

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