Numbers omitting digits in certain base expansions

2025/03/12 by Yavicoli, Alexia, Yu, Han · 1 citation
#11B25 #28A12 #28A78 #28A80 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2503.09528

Abstract

In DOI:10.1017/etds.2022.2 the author proved that for each integer k there is an implicit number M > 0 such that if b₁, ⋯ , b_k are multiplicatively independent integers greater than M, there are infinitely many integers whose base b₁, b₂, ⋯ , b_k expansions all do not have zero digits. In this paper we don't require the multiplicative independence condition and make the result quantitative, getting an explicit value for M. We also obtain a result for the case when the missing digit(s) may not be zero. Finally, we extend our method to study various missing-digit sets in an algebraic setting.

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