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On the expansion of some exponential periods in an integer base

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Abstract

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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  1. CNRS, Université de Lyon, Université Lyon 1, Institut Camille Jordan, 43 boulevard du 11 novembre 1918, 69622, Villeurbanne cedex, France

    Boris Adamczewski

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  1. Boris Adamczewski
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Correspondence to Boris Adamczewski.

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Adamczewski, B. On the expansion of some exponential periods in an integer base. Math. Ann. 346, 107–116 (2010). https://doi.org/10.1007/s00208-009-0391-z

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  • DOI: https://doi.org/10.1007/s00208-009-0391-z

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