Courier Corporation, May 14, 1997 - Mathematics - 95 pages
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.
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algebraic number apparatus of continued arbi arbitrary integers assertion basic basis of Theorem best approximation bounded elements CALCULUS OF VARIATIONS canonical representation Chapter completes the proof consequently continued frac continued fraction 13 continued fraction representing convergent infinite continued convergent of order countable set defined diverges Edwards Deming everywhere finite continued fraction finite number follows formula Gauss given continued fraction hence inequality 33 infinite set intermediate fractions interval of rank last element lemma Let us agree Liouville's theorem MATHEMATICAL measure theory measure zero mediant natural number numerator and denominator obtain obviously odd-order convergent order of approximation periodic continued fraction pk/qk polynomial positive number problem proof of Theorem properties quadratic irrational number rational number result rn+i satisfy the inequality second kind set of numbers solutions in integers sufficiently large Suppose systematic fractions Theorem 15 Theorem 29 Theorem 33 theory of continued tinued fraction tion unique vergent