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The Relative Growth Rate of the Partial Quotients

Author: ZuoZhiYong
Tutor: WuJun
School: Huazhong University of Science and Technology
Course: Basic mathematics
Keywords: Hausdorff measure Hausdorff dimension the continued fraction partial quotients
CLC: O174.12
Type: Master's thesis
Year: 2009
Downloads: 9
Quote: 0
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Abstract


In this note we look at the rate of growth of the partial quotients of the irrational number relative to the rate at which x is approximated by its rational convergents. For x∈(0,1) irrational, let pq be the sequence of rational convergen given by the continued fraction expansion of x . Here we study the Hausdorff dimension of exceptional sets on which different growth rates are achieved.

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Theory of functions > Real Analysis,Real Variable > Measure Theory
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