The number of extensions of a number field with fixed degree and bounded discriminant

2003/09/08 by Jordan S. Ellenberg, Ellenberg, Jordan S., Akshay Venkatesh +1
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.math/0309153

arxiv created 2003/09/08 · arxiv updated 2009/12/01

Abstract

We give an upper bound on the number of extensions of a fixed number field of prescribed degree and discriminant less than X; these bounds improve on work of Schmidt. We also prove various related results, such as lower bounds for the number of extensions and upper bounds for Galois extensions.

Related

• Counting G-Extensions by Discriminant
• Enumerating Galois extensions of number fields
• Upper bound on the number of extensions of a given number field
• Counting extensions of number fields with Frobenius Galois group
• Improved bounds on number fields of small degree