Continued fractions, normality, and the difficulty of multiplying by 2 | College of Science

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Continued fractions, normality, and the difficulty of multiplying by 2

Event Date: 
Monday, September 16, 2019 - 4:00pm
Location: 
GAB 461
Event Department: 

An expansion of a number is said to be normal if every finite string of digits in the expansion appears with a particular limiting frequency. For base-b expansions, the required frequency of a n-digit string should be b^{-n}. For continued fractions, the required frequency of a string is determined by the Gauss-Kuzmin statistics. It's known that certain operations preserve normality. For base-b expansions, multiplication and addition by non-zero rationals preserve normality. This is in part because the complexity of these operations in base-b is negligible. An exact notion of "low complexity operation" for continued fraction expansions has not been formulated, and even multiplication by 2 is a vastly more intricate procedure for continued fractions than base-b expansion, we nonetheless will show that multiplication and addition by non-zero rationals preserves normality for continued fraction expansions.

Presenter Name: 
Joseph Vandehey
Presenter Organization: 
UT Tyler

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