Florian Luca (Wits/Jeddah/Saarbrücken): A variation of a transcendence criterion

Austrian-Hungarian Diophantine Number Theory seminar
https://uni-salzburg.webex.com/uni-salzburg/j.php?MTID=m48611ae7aafae004ac6e1440a7e14fd2

Abstract: In this talk, we survey the transcendence criterion for automatic numbers due to Adamczewski, Bugeaud and Luca, and introduce additional conditions in order to make it more useful for particular instances. As a concrete application we prove that if b is algebraic, |b|≥1 and θ is real such that eiθ is algebraic but not a root of unity then ∑cos(nθ)/bn is transcendental, where the sum is taken over all n>0 with cos(nθ)>0. Further, if ρ is real quadratic and r∈ℚ, then ∑b-⌊nρ+r⌋ is transcendental, where the sum is taken over all n≥0. This is joint work with J. Ouaknine and J.B. Worrell.