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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Bibliographic Details
Published inMathematische annalen Vol. 346; no. 1; pp. 107 - 116
Main Author Adamczewski, Boris
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer-Verlag 01.01.2010
Springer Verlag
Subjects
Mathematics
Mathematics and Statistics
Number Theory
Algebraic Number
Positive Real Number
Diophantine Approximation
Partial Quotient
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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.
ISSN:0025-5831
1432-1807
DOI:10.1007/s00208-009-0391-z