Abstract. We describe practical algorithms from computational algebraic number theory, with applications to class field theory. These include basic arithmetic, approximation and uniformizers,...
ERROR ESTIMATES FOR THE DAVENPORT-HEILBRONN THEOREMS (2008)
Karim Belabas, Manjul Bhargava, Carl Pomerance
Abstract. We improve the known remainder terms for the theorems of Davenport and Heilbronn on the density of discriminants of cubic fields and average 3-torsion in the class group of quadratic...
COMPUTING THE TAME KERNEL OF QUADRATIC IMAGINARY FIELDS JERZY BROWKIN, (2008)
Abstract. J. Tate has determined the group K2OF (called the tame kernel) for six quadratic imaginary number fields F = Q ( √ d), where d = −3, −4, −7, −8, −11, −15. Modifying the method...
SMALL GENERATORS OF THE IDEAL CLASS GROUP (2008)
Karim Belabas, Francisco Diaz, Y Diaz, Eduardo Friedman
Abstract. Assuming the Generalized Riemann Hypothesis, Bach has shown that the ideal class group CℓK of a number field K can be generated by the prime ideals of K having norm smaller than 12 �...
Karim Belabas, Francisco Diaz, Y Diaz, Eduardo Friedman
Abstract. Assuming the Generalized Riemann Hypothesis, Bach has shown that the ideal class group CℓK of a number field K can be generated by the prime ideals of K having norm smaller than 12 �...
Article electronically published on January 30, 2004 ON QUADRATIC FIELDS WITH LARGE 3-RANK (2008)
Abstract. 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...
GENERATORS AND RELATIONS FOR K 2 OF, F IMAGINARY QUADRATIC (2007)
Abstract. Tate's algorithm [31] for computing K 2 OF for rings of integers in a number eld has been adapted for the computer and gives explicit generators for the group and sharp bounds on their...
A relative van Hoeij algorithm over number fields (2004)
Abstract. Van Hoeij’s algorithm for factoring univariate polynomials over the rational integers rests on the same principle as Berlekamp-Zassenhaus, but uses lattice basis reduction to improve...
Tuning and Generalizing Van Hoeij's Algorithm (2001)
Belabas, Karim, Hanrot, Guillaume, Zimmermann, Paul
Recently, van Hoeij's published a new algorithm for factoring polynomials over the rational integers [11]. This algorithms rests on the same principle as Berlekamp-Zassenhaus [2, 13], but uses...
Tuning and Generalizing Van Hoeij's Algorithm (2001)
Belabas, Karim, Hanrot, Guillaume, Zimmermann, Paul
Recently, van Hoeij's published a new algorithm for factoring polynomials over the rational integers [11]. This algorithms rests on the same principle as Berlekamp-Zassenhaus [2, 13], but uses...
Tuning and Generalizing Van Hoeij's Algorithm (2001)
Belabas, Karim, Hanrot, Guillaume, Zimmermann, Paul
Recently, van Hoeij's published a new algorithm for factoring polynomials over the rational integers [11]. This algorithms rests on the same principle as Berlekamp-Zassenhaus [2, 13], but uses...
On the mean 3-rank of quadratic fields (1999)
Abstract. 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...
On quadratic fields with large 3-rank (1993)
Abstract. 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...