The refined Diophantine exponent and its applications in transcendental number theory

par Khai Nguyen (ICJ - Lyon 1)

mardi 2 juin 2026, 10:45 → 11:45 Europe/Paris

Salle Fokko du Cloux (ICJ, Université Lyon 1)

In 2007, Adamczewski and Bugeaud introduced the notion of the Diophantine exponent of an infinite word as a quantitative measure of repetition, leading to strong transcendence results. In this talk, by allowing some form of noise, we introduce the refined Diophantine exponent and use it to obtain transcendence results and transcendence measures in the sense of Mahler's classification. This notion is also inspired by the work of Corvaja and Zannier on lacunary sequences; Kebis, Luca, Ouaknine, Scoones, and Worrell on Sturmian words and k-bonacci words; and Bell, Diller, and Jonsson on transcendental dynamical degrees.