Counting G-Extensions by Discriminant

2017/04/11 by Dummit, Evan P. · 1 citation
#11H06 (Secondary) #11R21 (Primary) #11R29 #13A50 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1704.03124

Abstract

The problem of analyzing the number of number field extensions L/K with bounded (relative) discriminant has been the subject of renewed interest in recent years, with significant advances made by Schmidt, Ellenberg-Venkatesh, Bhargava, Bhargava-Shankar-Wang, and others. In this paper, we use the geometry of numbers and invariant theory of finite groups, in a manner similar to Ellenberg and Venkatesh, to give an upper bound on the number of extensions L/K with fixed degree, bounded relative discriminant, and specified Galois closure.

Cited by

• Counting C₂ \wr S₄ fields with a power saving error term

Related

• The number of extensions of a number field with fixed degree and bounded discriminant
• Enumerating Galois extensions of number fields
• Counting extensions of number fields with Frobenius Galois group
• Upper bound on the number of extensions of a given number field
• Inductive methods for counting number fields