Lévy constants of transcendental numbers
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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 $\alpha$.References
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Additional Information
- Christoph Baxa
- Affiliation: Department of Mathematics, University of Vienna, Nordbergstraße 15, A-1090, Wien, Austria
- Email: christoph.baxa@univie.ac.at
- Received by editor(s): August 26, 2008
- Received by editor(s) in revised form: September 29, 2008
- Published electronically: January 28, 2009
- Communicated by: Ken Ono
- © Copyright 2009 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 137 (2009), 2243-2249
- MSC (2000): Primary 11K50, 11J81
- DOI: https://doi.org/10.1090/S0002-9939-09-09787-1
- MathSciNet review: 2495257