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CONTINUED FRACTIONS
by Andrew M Rockett (Long Island University) & Peter Szüsz (State University of NewYork, Stony Brook)
This book presents the arithmetic and metrical theory of regular continued fractions and is intended to be a modern version of A. Ya. Khintchine's classic of the same title. Besides new and simpler proofs for many of the standard topics, numerous numerical examples and applications are included (the continued fraction of e, Ostrowski representations and t-expansions, period lengths of quadratic surds, the general Pell's equation, homogeneous and inhomogeneous diophantine approximation, Hall's theorem, the Lagrange and Markov spectra, asymmetric approximation, etc). Suitable for upper level undergraduate and beginning graduate students, the presentation is self-contained and the metrical results are developed as strong laws of large numbers.
Contents:
- Introduction
- The Law of Best Approximation
- Periodic Continued Fractions
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Applications
- Metrical Theory
- Applications to Metrical Diophantine Approximation Notes
Readership: Advanced undergraduates, graduates and mathematicians.
"There are just a few, mostly aged books on continued fractions available. This one promises to have an enriching and stimulating effect on the way the subject presents itself to students and professional mathematicians alike."
Ch. Baxa, Wien
Monatshefte fur Mathematik, 1993 |
| 200pp |
Pub. date: Aug 1992 |
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