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math.NT2010★ 5 cited
Schanuel's conjecture and algebraic powers z^w and w^z with z and w transcendental
Diego Marques, Jonathan Sondow
We give a brief history of transcendental number theory, including Schanuel's conjecture (S). Assuming (S), we prove that if z and w are complex numbers, not 0 or 1, with z^w and w…
math.NT2010
Some transcendental functions with an empty exceptional set
D. Marques, F. M. S. Lima
A transcendental function usually returns transcendental values at algebraic points. The (algebraic) exceptions form the so-called \emph{exceptional set}, as for instance the unita…