Effective irrationality measures for real and p-adic roots of rational numbers close to 1, with an application to parametric families of Thue–Mahler equations

• Published in: Mathematical proceedings of the Cambridge Philosophical Society Vol. 164; no. 1; pp. 99 - 108
• Main Author: BUGEAUD, YANN
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 01.01.2018; Cambridge University Press (CUP)
• Subjects: Irrationality; Logarithms; Mathematical analysis; Mathematics; Number Theory; Numbers

We show how the theory of linear forms in two logarithms allows one to get very good effective irrationality measures for nth roots of rational numbers a/b, when a is very close to b. We give a p-adic analogue of this result under the assumption that a is p-adically very close to b, that is, that a...