Some applications of the p-adic analytic subgroup theorem

الأصل · EN

We use a p-adic analogue of the analytic subgroup theorem of Wüstholz to deduce the transcendence and linear independence of some new classes of p-adic numbers. In particular we give p-adic analogues of results of Wüstholz contained in [G. Wüstholz, Some remarks on a conjecture of Waldschmidt, Diophantine approximations and transcendental numbers, Progress in Mathematics 31, Birkhäuser Boston, Boston, MA, (1983), 329-336] and generalizations of results obtained by Bertrand in [D. Bertrand, Sous-groupes à un paramètre p-adique de variétés de groupe, Invent. Math. 40 (1977), no. 2, 171-193] and [D. Bertrand, Problèmes locaux, Société Mathématique de France, Astérisque 60-70 (1979), 163-189].