A note on $p$-rational fields and the abc-conjecture
Number Theory
2019-07-09 v2
Abstract
In this short note we confirm the relation between the generalized -conjecture and the -rationality of number fields. Namely, we prove that given K a real quadratic extension or an imaginary -extension, if the generalized -conjecture holds in K, then there exist at least prime numbers for which K is -rational, here is some nonzero constant depending on K. The real quadratic case was recently suggested by B\"ockle-Guiraud-Kalyanswamy-Khare.
Cite
@article{arxiv.1903.11271,
title = {A note on $p$-rational fields and the abc-conjecture},
author = {Christian Maire and Marine Rougnant},
journal= {arXiv preprint arXiv:1903.11271},
year = {2019}
}