A NOTE ON p-RATIONAL FIELDS AND THE ABC-CONJECTURE
| Affiliation auteurs | Affiliation ok |
| Titre | A NOTE ON p-RATIONAL FIELDS AND THE ABC-CONJECTURE |
| Type de publication | Journal Article |
| Year of Publication | 2020 |
| Auteurs | Maire C, Rougnant M |
| Journal | PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY |
| Volume | 148 |
| Pagination | 3263-3271 |
| Date Published | AUG |
| Type of Article | Article |
| ISSN | 0002-9939 |
| Mots-clés | abc-conjecture, p-rationals fields |
| 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 S-3-extension, if the generalized abc-conjecture holds in K, then there exist at least c log X prime numbers p <= X for which K is p-rational; here c is some nonzero constant depending on K. The real quadratic case was recently suggested by Bockle-Guiraud-Kalyanswamy-K hare. |
| DOI | 10.1090/proc/14983 |