Continued Fractions

Anneli Lax New Mathematical Library

by Carl D. Olds, A. Rockett, P. Szusze

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.

Genres: Mathematics

196 pages, Paperback

First published January 1, 1963

Reviews

[Riccardo · Rating 5 out of 5]

Ottimo libro, scritto (e tradotto) con uno stile molto scorrevole e semplice da capire. Molti esercizi ed esempi, perfetto come introduzione alla teoria delle frazioni continue. Assolutamente consigliato.

[Will · Rating 4 out of 5]

Introduction to (simple) continued fractions. Convergents as lower and upper bound rational approximations. Finite = rational number. Periodic = quadratic irrational (Lagrange). Applications to Diophantine problems such as Ax+By=C, Pell's x^2-Ny^2=1. Shanks' method for logarithms was interesting.