Transcendence of Sturmian Numbers over an Algebraic Base

Florian Luca, Joel Ouaknine, James Worrell

We consider numbers of the form $S_{\beta }(\mathbf{u}):={\sum }_{n=0}^{\infty }\frac{u_n}{{\beta }^n}$ for $\mathbf{u}=⟨u_n{⟩}_{n=0}^{\infty }$ a Sturmian sequence over a binary alp…