11 citations · 13 across the 3 of their papers we have counts for
5 papers
A counter example to Malle's conjecture on the asymptotics of discriminants
Juergen Klueners
In this note we give a counter example to a conjecture of Malle which predicts the asymptotic behaviour of the counting functions for field extensions with given Galois group and b…
The number of fields with given discriminant
Juergen Klueners
We prove that the number of quartic --extensions of the rationals of given discriminant is $O_\eps(d^{1/2+\eps})$ for all $\eps>0$. For a prime number we derive that t…
Factoring polynomials over global fields
K. Belabas, M. van Hoeij, J. Klueners +1
Let K be a global field and f in K[X] be a polynomial. We present an efficient algorithm which factors f in polynomial time.
Counting nilpotent Galois extensions
Juergen Klueners, Gunter Malle
We obtain strong information on the asymptotic behaviour of the counting function for nilpotent Galois extensions with bounded discriminant of arbitrary number fields. This extends…
A database for field extensions of the rationals
Juergen Klueners, Gunter Malle
We report on a database of field extensions of the rationals, its properties and the methods used to compute it. At the moment the database encompasses roughly 100,000 polynomials…