On the beta-expansions of 1 and algebraic numbers for a Salem number beta
抄録
<jats:title>Abstract</jats:title><jats:p>We study the digits of <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0143385713000990_inline1" /><jats:tex-math>$\beta $</jats:tex-math></jats:alternatives></jats:inline-formula>-expansions in the case where <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0143385713000990_inline2" /><jats:tex-math>$\beta $</jats:tex-math></jats:alternatives></jats:inline-formula> is a Salem number. We introduce new upper bounds for the numbers of occurrences of consecutive 0s in the expansion of 1. We also give lower bounds for the numbers of non-zero digits in the <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" xlink:type="simple" xlink:href="S0143385713000990_inline3" /><jats:tex-math>$\beta $</jats:tex-math></jats:alternatives></jats:inline-formula>-expansions of algebraic numbers. As applications, we give criteria for transcendence of the values of power series at certain algebraic points.</jats:p>
収録刊行物
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- Ergodic Theory and Dynamical Systems
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Ergodic Theory and Dynamical Systems 35 (4), 1243-1262, 2014-02-26
Cambridge University Press (CUP)
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詳細情報 詳細情報について
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- CRID
- 1360285707977532416
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- ISSN
- 14694417
- 01433857
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