Algebraic and transcendental solutions of some exponential equations

Details Algebraic and transcendental solutions of some exponential equations Algebraic and transcendental solutions of some exponential equations

2011-08-30

arxiv.org/abs/1108.6096v2

Annales Mathematicae et Informaticae 37 (2010) 151-164

Mathematics

Number Theory

14 pages, 7 figures, corrected top of p. 4

Scientific paper

We study algebraic and transcendental powers of positive real numbers, including solutions of each of the equations $x^x=y$, $x^y=y^x$, $x^x=y^y$, $x^y=y$, and $x^{x^y}=y$. Applications to values of the iterated exponential functions are given. The main tools used are classical theorems of Hermite-Lindemann and Gelfond-Schneider, together with solutions of exponential Diophantine equations.

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