On the numbers $e^e, e^{e^2}$ and $e^{\pi^2}$.
Waldschmidt, Michel
HAL, hal-01109388 / Harvested from HAL
Text on HAL
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.
Publié le : 1998-07-04
Classification:  Transcendental numbers,  Algebraic independence,  simultaneous approximation,  Gelfond's method,  Schneider's problems,  Schanuel's Conjecture,  [MATH]Mathematics [math] 
@article{hal-01109388,
     author = {Waldschmidt, Michel},
     title = {On the numbers $e^e, e^{e^2}$ and $e^{\pi^2}$.},
     journal = {HAL},
     volume = {1998},
     number = {0},
     year = {1998},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-01109388}
}

Waldschmidt, Michel. On the numbers $e^e, e^{e^2}$ and $e^{\pi^2}$.. HAL, Tome 1998 (1998) no. 0, . http://gdmltest.u-ga.fr/item/hal-01109388/