On the expansion of some exponential periods in an integer base
We derive a lower bound for the subword complexity of the base- b expansion ( b ≥ 2) of all real numbers whose irrationality exponent is equal to 2. This provides a generalization of a theorem due to Ferenczi and Mauduit. As a consequence, we obtain the first lower bound for the subword complexity o...
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Published in | Mathematische annalen Vol. 346; no. 1; pp. 107 - 116 |
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Main Author | |
Format | Journal Article |
Language | English |
Published |
Berlin/Heidelberg
Springer-Verlag
01.01.2010
Springer Verlag |
Subjects | |
Online Access | Get full text |
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Summary: | We derive a lower bound for the subword complexity of the base-
b
expansion (
b
≥ 2) of all real numbers whose irrationality exponent is equal to 2. This provides a generalization of a theorem due to Ferenczi and Mauduit. As a consequence, we obtain the first lower bound for the subword complexity of the number
e
and of some other transcendental exponential periods. |
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ISSN: | 0025-5831 1432-1807 |
DOI: | 10.1007/s00208-009-0391-z |