Explicit Approximations to Class Field Towers

TL;DR

This paper constructs infinite families of number fields with controlled root discriminants, addressing a question about class field towers and their boundedness properties.

Contribution

It provides an explicit, efficient method to build infinite number field families with root discriminants bounded by a small power of the degree, advancing understanding of class field towers.

Findings

Constructed infinite families of number fields with bounded root discriminants.

Provided an explicit method for such constructions for any epsilon > 0.

Addressed and answered a question posed by Peikert and Rosen.

Abstract

We answer a question of Peikert and Rosen by giving for each $\epsilon > 0$ an efficient construction of infinite families of number fields $N$ such that the root discriminant $D_N^{1/[N:\mathbb{Q}]}$ is bounded above by a constant times $[N:\mathbb{Q}]^\epsilon$.