On the numbers $e^e, e^{e^2}$ and $e^{\pi^2}$.

Michel Waldschmidt (1)

1 IMJ - Institut de Mathématiques de Jussieu

We give two measures of simultaneous approximation by algebraic numbers, the first one for the triple $( e, e^e, e^{e^2})$ and the second one for $(\pi, e, e^{\pi^2})$. We deduce from these measures two transcendence results which had been proved in the early 70's by W. D. Brownawell and the author.

Mots clés: Transcendental numbers; Algebraic independence; simultaneous approximation; Gelfond's method; Schneider's problems; Schanuel's Conjecture

Domaines: Mathématiques [math]

Michel Waldschmidt. On the numbers $e^e, e^{e^2}$ and $e^{\pi^2}$.. Hardy-Ramanujan Journal, 1998, pp.27 - 34. ⟨hal-01109388⟩