A note on $p$-rational fields and the abc-conjecture
Résumé
In this short note we confirm the relation between the generalized abc-conjecture and the p-rationality of number fields. Namely, we prove that given K{Q a real quadratic extension or an imaginary dihedral extension of degree 6, if the generalized abc-conjecture holds in K, then there exist at least c logX prime numbers p ď X for which K is p-rational, here c is some nonzero constant depending on K. The real quadratic case was recently suggested by Böckle-Guiraud-Kalyanswamy-Khare.
Domaines
Théorie des nombres [math.NT]Origine | Fichiers produits par l'(les) auteur(s) |
---|
Loading...