Infinite class field tower with small root discriminant

2024/06/02 by Qi Liu, Liu, Qi, Zugan Xing +1
Engineering · #11R29 #11R37 #Dam Engineering and Safety #FOS: Mathematics #Hydraulic flow and structures #Number Theory (math.NT) #Power Systems Fault Detection

paper · pdf · doi:10.48550/arxiv.2406.00797

openalex publication_date 2024/06/02 · openalex created_date 2024/06/07 · openalex updated_date 2026/07/28

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 p-class field tower when p=3, 5, 7.

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