Tokyo Journal of Mathematics

A Diophantine Approximation of $e^{1/s}$ in Terms of Integrals

Takao KOMATSU

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Abstract

Let $p_n/q_n$ be the $n$-th convergent of the continued fraction expansion of a real number $\alpha$. It is known that $|p_n-q_n\alpha|$ is very small tending to $0$ as $n$ tends to infinity. In this paper we establish a method how to express $p_n-q_n\alpha$ in terms of integrals when $\alpha$ is an $e$-type real number and its continued fraction expansion is quasi-periodic.

Article information

Source
Tokyo J. Math., Volume 32, Number 1 (2009), 159-176.

Dates
First available in Project Euclid: 7 August 2009

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1249648415

Digital Object Identifier
doi:10.3836/tjm/1249648415

Mathematical Reviews number (MathSciNet)
MR2541162

Zentralblatt MATH identifier
1241.11076

Citation

KOMATSU, Takao. A Diophantine Approximation of $e^{1/s}$ in Terms of Integrals. Tokyo J. Math. 32 (2009), no. 1, 159--176. doi:10.3836/tjm/1249648415. https://projecteuclid.org/euclid.tjm/1249648415


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