The diophantine approximation of certain continued fractions
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- by Charles F. Osgood PDF
- Proc. Amer. Math. Soc. 36 (1972), 1-7 Request permission
Abstract:
Given a real number $\alpha$ defined by \[ \frac {1}{{\varphi (1) + }}\frac {1}{{\varphi (2) + }} \cdots ,\] where $\varphi$ is a function from the natural numbers to the rational numbers larger than or equal to one which satisfies certain restrictions on the growth of the numerators and denominators of the numbers $\varphi (n)$, then a lower bound is found in terms of $\varphi$ for the diophantine approximation of $\alpha$.References
- A. Ya. Khinchin, Continued fractions, University of Chicago Press, Chicago, Ill.-London, 1964. MR 0161833
- Charles F. Osgood, On the diophantine approximation of values of functions satisfying certain linear $q$-difference equations, J. Number Theory 3 (1971), 159–177. MR 277481, DOI 10.1016/0022-314X(71)90033-3
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 36 (1972), 1-7
- MSC: Primary 10F05
- DOI: https://doi.org/10.1090/S0002-9939-1972-0308059-X
- MathSciNet review: 0308059