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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Lévy constants of transcendental numbers


Author: Christoph Baxa
Journal: Proc. Amer. Math. Soc. 137 (2009), 2243-2249
MSC (2000): Primary 11K50, 11J81
Published electronically: January 28, 2009
MathSciNet review: 2495257
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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 $.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09787-1
PII: S 0002-9939(09)09787-1
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
Article copyright: © Copyright 2009 American Mathematical Society