Continued fractions. Translated by Peter Wynn. (English) Zbl 0117.28503

Khintchine, A. Ya.

Groningen, The Netherlands: P. Noordhoff, Ltd. 101 pp. (1963).

This is another translation into English of the third Russian edition (see the following title Zbl 0117.28601; also the German translation “Kettenbrüche”, Leipzig: B. G. Teubner (1956; Zbl 0071.03601). The third Russian edition was reprinted from the second (1949; Zbl 0037.32503) with only a few brief bibliographical remarks added. Aside from these notes there is no bibliography. The second Russian edition appeared in 1949 with no essential changes from the first edition in 1935 (JFM 63.0924.02).
As in the other translations, Chapter I is concerned with the elementary recurrence relations. Chapter II deals with the real number system constructed from continued fractions; regular continued fractions and other problems are treated. Chapter III is concerned with a presentation of the metric theory of continued fractions.

Reviewer: Evelyn Frank (Chicago)

MSC:

11-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory
11A55	Continued fractions
11J70	Continued fractions and generalizations
11K50	Metric theory of continued fractions
11B37	Recurrences

Keywords:

elementary recurrence relations; real number system constructed from continued fractions; regular continued fractions; metric theory of continued fractions

Citations:

Zbl 0117.28601; Zbl 0071.03601; Zbl 0037.32503; JFM 63.0924.02