Lévy constants of transcendental numbers

Baxa, Christoph

doi:10.1090/S0002-9939-09-09787-1

Lévy constants of transcendental numbers
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by Christoph Baxa PDF

Proc. Amer. Math. Soc. 137 (2009), 2243-2249 Request permission

Abstract:

We prove that every $\gamma \ge \log \frac {1+\sqrt 5}{2}$ is the Lévy constant of a transcendental number; i.e., there exists a transcendental number $\alpha$ such that $\gamma =$ ${\lim \limits _{m\to \infty }}\frac {1}{m}\log q_{m}(\alpha )$, where $q_{m}(\alpha )$ denotes the denominator of the $m$th convergent of $\alpha$.

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