Some new infinite families of non-$p$-rational real quadratic fields
Abstract
Fix a finite collection of primes , not containing or . Using some observations which arose from attempts to solve the SIC-POVMs problem in quantum information, we give a simple methodology for constructing an infinite family of simultaneously non--rational real quadratic fields, unramified above any of the . Alternatively these may be described as infinite sequences of instances of , for varying , where every is a -Wall-Sun-Sun prime, or equivalently a generalised Fibonacci-Wieferich prime. One feature of these techniques is that they may be used to yield fields for which a -power cyclic component of the torsion group of the Galois groups of the maximal abelian pro--extension of unramified outside primes above , is of size for arbitrarily large.
Keywords
Cite
@article{arxiv.2406.14632,
title = {Some new infinite families of non-$p$-rational real quadratic fields},
author = {Gary McConnell},
journal= {arXiv preprint arXiv:2406.14632},
year = {2024}
}
Comments
11 pages