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- Publications
- Influence

A fast algorithm to compute cubic fields

- K. Belabas
- Mathematics, Computer Science
- Math. Comput.
- 1 July 1997

We present a very fast algorithm to build up tables of cubic fields. Real cubic fields with discriminant up to 10 11 and complex cubic fields down to -10 11 have been computed.

User’s Guide to PARI / GP

- C. Batut, K. Belabas, D. Bernardi, H. Cohen, M. Olivier
- Mathematics
- 2000

- 137
- 8
- PDF

A relative van Hoeij algorithm over number fields

- K. Belabas
- Computer Science, Mathematics
- J. Symb. Comput.
- 1 May 2004

Abstract van Hoeij’s algorithm for factoring univariate polynomials over the rational integers rests on the same principle as the Berlekamp–Zassenhaus algorithm, but uses lattice basis reduction to… Expand

The logarithmic class group package in PARI/GP

- K. Belabas, Jean-François Jaulent
- Mathematics
- 2016

This note presents our implementation in the PARI/GP system of the various arithmetic invariants attached to logarithmic classes and units of number fields. Our algorithms simplify and improve on… Expand

Error estimates for the Davenport-Heilbronn theorems

- K. Belabas, M. Bhargava, C. Pomerance
- Mathematics
- 15 May 2010

We obtain the first known power-saving remainder terms for the theorems of Davenport and Heilbronn on the density of discriminants of cubic fields and the mean number of 3-torsion elements in the… Expand

Generators and relations for K_2 O_F.

- K. Belabas, H. Gangl
- Mathematics
- 1 March 2004

Tate's algorithm for computing K_2 O_F for rings of integers in a number field has been adapted for the computer and gives explicit generators for the group and sharp bounds on their order---the… Expand

On quadratic fields with large 3-rank

- K. Belabas
- Computer Science, Mathematics
- Math. Comput.
- 30 January 2004

Davenport and Heilbronn defined a bijection between classes of binary cubic forms and classes of cubic fields, which has been used to tabulate the latter. We give a simpler proof of their theorem,… Expand

Crible et 3-rang des corps quadratiques

- K. Belabas
- Mathematics
- 1996

Resume. Considerons le cardinal h∗ 3 (∆) de l’ensemble des racines cubiques de l’unite dans le groupe des classes de Q( √ ∆), ou ∆ est un discriminant fondamental. Un resultat de Davenport et… Expand

Topics in computational algebraic number theory

- K. Belabas
- Mathematics
- 2004

We describe practical algorithms from computational algebraic number theory, with applications to class field theory. These include basic arithmetic, approximation and uniformizers, discrete… Expand

On the Mean 3-Rank of Quadratic Fields

- K. Belabas
- Mathematics
- 1 August 1999

The Cohen–Lenstra–Martinet heuristics give precise predictions about the class groups of a ‘random’ number field. The 3-rank of quadratic fields is one of the few instances where these have been… Expand