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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Computable absolutely normal numbers and discrepancies

Author: Adrian-Maria Scheerer
Journal: Math. Comp. 86 (2017), 2911-2926
MSC (2010): Primary 11K16; Secondary 11Y16
Published electronically: May 17, 2017
MathSciNet review: 3667030
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Abstract: We analyze algorithms that output absolutely normal numbers digit-by-digit with respect to quality of convergence to normality of the output, measured by the discrepancy. We consider explicit variants of algorithms by Sierpinski, by Turing and an adaption of constructive work on normal numbers by Schmidt. There seems to be a trade-off between the complexity of the algorithm and the speed of convergence to normality of the output.

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Additional Information

Adrian-Maria Scheerer
Affiliation: Institute of Analysis and Number Theory, Graz University of Technology , Kopernikusgasse 24/II, 8010 Graz, Austria

Received by editor(s): January 19, 2016
Received by editor(s) in revised form: May 15, 2016
Published electronically: May 17, 2017
Article copyright: © Copyright 2017 American Mathematical Society