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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



The diophantine approximation of certain continued fractions

Author: Charles F. Osgood
Journal: Proc. Amer. Math. Soc. 36 (1972), 1-7
MSC: Primary 10F05
MathSciNet review: 0308059
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Abstract: Given a real number $ \alpha $ defined by

$\displaystyle \frac{1}{{\varphi (1) + }}\frac{1}{{\varphi (2) + }} \cdots ,$

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 [Enhancements On Off] (What's this?)

  • [1] A. Ya. Khinchin, Continued fractions, The University of Chicago Press, Chicago, Ill.-London, 1964. MR 0161833
  • [2] 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 0277481

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Keywords: Diophantine approximation, continued fractions, rational partial quotients
Article copyright: © Copyright 1972 American Mathematical Society