English

Infinite class field tower with small root discriminant

Number Theory 2024-06-07 v2

Abstract

We generalize Schoof's theorem in 1986 and apply this to construct a class of Kummer extensions of the cyclotomic fields with infinite class tower. As an application, we give some number fields with a small root discriminant, which has an infinite pp-class field tower when p=3,5,7p=3, 5, 7.

Cite

@article{arxiv.2406.00797,
  title  = {Infinite class field tower with small root discriminant},
  author = {Qi Liu and Zugan Xing},
  journal= {arXiv preprint arXiv:2406.00797},
  year   = {2024}
}

Comments

9 pages

R2 v1 2026-06-28T16:50:12.970Z