Abstract
We prove that these Cantor sets are made up of transcendental numbers, up to their endpoints 0 and 1, under some arithmetical assumptions on the data. To that purpose, we establish a criterion of linear independence over the field of algebraic numbers for the three numbers 1; ∈1; ∈2, where ∈1 and ∈2 are two arbitrary Sturmian numbers with the same slope.
Original language | English |
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Pages (from-to) | 1691-1704 |
Number of pages | 14 |
Journal | Annali della Scuola Normale Superiore di Pisa - Classe di Scienze |
Volume | 22 |
Issue number | 4 |
DOIs | |
State | Published - 2021 |