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Abstract: Let ` be a real number with continued fraction expansion ` = [a 0 ; a 1 ; a 2 ; : : :], and let M = " a b c d # be a matrix with integer entries and with j det(M)j 6= 0. If ` has bounded partial quotients, then a`+b c`+d = [a 0 ; a 1 ; a 2 ; : : :] also has bounded partial quotients. More precisely, if a j K for all sufficiently large j, then a j j det(M)j(K + 2) for all sufficiently large j. We also give a weaker bound valid for all a j with j 1. 1991 Mathematics... (Update)
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BibTeX entry: (Update)
@misc{ lagarias-linear,
author = "J. C. Lagarias and J. O. Shallit",
title = "Linear Fractional Transformations of Continued Fractions with Bounded Partial
Quotients",
url = "citeseer.ist.psu.edu/lagarias96linear.html" }
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