On two notions of complexity of algebraic numbers
Yann Bugeaud, Jan-Hendrik Evertse
TL;DR
This paper improves lower bounds on the complexity of algebraic numbers' digit sequences using advanced number theory tools, specifically the Subspace Theorem, to deepen understanding of their structural properties.
Contribution
It introduces new, sharper lower bounds for the block complexity and digit changes in the expansions of irrational algebraic numbers, employing a quantitative form of the Subspace Theorem.
Findings
Enhanced lower bounds for block complexity of algebraic numbers
Improved bounds on digit changes in b-ary expansions
Application of a quantitative Subspace Theorem to complexity measures
Abstract
we derive new, improved lower bounds for the block complexity of an irrational algebraic number and for the number of digit changes in the b-ary expansion of an irrational algebraic number. To this end, we apply a quantitative version of the Subspace Theorem due to Evertse and Schlickewei (2002).
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