b-ary expansions of algebraic numbers

2017/01/30 by Xianzu Lin, Lin, Xianzu
Mathematics · #11A63 #11K16 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11A63 #msc:11K16

paper · pdf · doi:10.48550/arxiv.1701.08503

15 pages. Any comments are very welcome

arxiv created 2017/01/30 · arxiv updated 2017/01/31

Abstract

In this paper we give a generalization of the main results in \citeab,ab1 about b-ary expansions of algebraic numbers. As a byproduct we get a large class of new transcendence criteria. One of our corollaries implies that b-ary expansions of linearly independent irrational algebraic numbers are quite independent. Motivated by this result, we propose a generalized Borel conjecture.

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