Description

Book Synopsis
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.

Table of Contents
Introduction; the law of best approximation; periodic continued fractions; applications; metrical theory; applications to metrical diophantine approximation.

Continued Fractions

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    A Paperback / softback by Andrew M Rockett, Peter Szusz

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      Publisher: World Scientific Publishing Co Pte Ltd
      Publication Date: Publication Date: 01/08/1992
      ISBN13: 9789810210526, 978-9810210526
      ISBN10: 9810210523

      Description

      Book Synopsis
      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.

      Table of Contents
      Introduction; the law of best approximation; periodic continued fractions; applications; metrical theory; applications to metrical diophantine approximation.

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