| Continued Fractions (1997) |
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| Elementary-level text by noted Soviet mathematician offers superb introduction to positive-integral elements of theory of continued fractions. Clear, straightforward presentation of the properties of the apparatus, the representation of numbers by continued fractions and the measure theory of continued fractions. 1964 edition. Prefaces. Table of Contents 1 Properties of the Apparatus 1.1 Introduction 1.2 Convergents 1.3 Infinite continued fractions 1.4 Continued fractions with natural elements 2 The Representation of Numbers by Continued Fractions 2.1 Continued fractions as an apparatus for representing real numbers 2.2 Convergents as best approximations 2.3 The order of approximation 2.4 General approximation theorems 2.5 The approximation of algebraic irrational numbers and Liouville's transcendental numbers 2.6 Quadratic irrational numbers and periodic continued fractions 3 The Measure Theory of Continued Fractions 3.1 Introduction 3.2 The elements as functions of the number represented 3.3 Measure-theoretic evaluation of the increase in the elements 3.4 Measure-theoretic evaluation of the increase in the denominators of the convergents. The fundamental theorem of the measure theory of approximation 3.5 Gauss's problem and Kuz'min's theorem 3.6 Average values 4 Index |
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| Notes |
| Originally published: Chicago : University of Chicago Press, 1964. "The English translation was edited by Herbert Eagle"--T.p. verso. Includes index. |