Explicit Approximations to Class Field Towers

Abstract

We answer a question of Peikert and Rosen by giving for each $\hat{I}\mu >0$ 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 $[N:\mathbb{Q}{]}^{\hat{I}}\mu$.

14 pages; we wrote a new section 5 relating our constructions to Redei symbols