Experimental Mathematics

On the Distribution of Galois Groups, II

Gunter Malle

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Abstract

We propose a very precise conjecture on the asymptotics of the counting function for extensions of number fields with fixed Galois group and bounded norm of the discriminant. This sharpens a previous conjecture of the author. The conjecture is known to hold for abelian groups and a few nonabelian ones. We give a heuristic argument why the conjecture should be true. We also present some computational data for the nonsolvable groups of degree 5.

Article information

Source
Experiment. Math., Volume 13, Issue 2 (2004), 129-136.

Dates
First available in Project Euclid: 20 July 2004

Permanent link to this document
https://projecteuclid.org/euclid.em/1090350928

Mathematical Reviews number (MathSciNet)
MR1884706

Zentralblatt MATH identifier
1099.11065

Subjects
Primary: 11R32: Galois theory 11R29: Class numbers, class groups, discriminants 12-04: Explicit machine computation and programs (not the theory of computation or programming)

Keywords
Galois groups density of extensions distribution of discriminants

Citation

Malle, Gunter. On the Distribution of Galois Groups, II. Experiment. Math. 13 (2004), no. 2, 129--136. https://projecteuclid.org/euclid.em/1090350928


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