On the number of nonzero digits in the beta-expansions of algebraic numbers
Rendiconti del Seminario Matematico della Università di Padova, Tome 136 (2016), pp. 205-223.

Many mathematicians have investigated the base-b expansions for integral base-b2, and more general β-expansions for a real number β>1. However, little is known on the β-expansions of algebraic numbers. The main purpose of this paper is to give new lower bounds for the numbers of nonzero digits in the β-expansions of algebraic numbers under the assumption that β is a Pisot or Salem number. As a consequence of our main results, we study the arithmetical properties of power series n=1 β -κ(z;n) , where z>1 is a real number and κ(z;n)=n z .

DOI : 10.4171/RSMUP/136-14
Classification : 11, 05, 14
Mots clés : Beta expansions, nonzero digits, Pisot numbers, Salem numbers
Kaneko, Hajme 1

1 University of Tsukuba, TSUKUBA, IBARAKI, JAPAN
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     title = {On the number of nonzero digits in the beta-expansions of algebraic numbers},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {205--223},
     publisher = {European Mathematical Society Publishing House},
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Kaneko, Hajme. On the number of nonzero digits in the beta-expansions of algebraic numbers. Rendiconti del Seminario Matematico della Università di Padova, Tome 136 (2016), pp. 205-223. doi : 10.4171/RSMUP/136-14. http://www.numdam.org/articles/10.4171/RSMUP/136-14/

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