Diophantine approximations of infinite series and products. (English) Zbl 1391.11083

Kolouch, Ondřej; Novotný, Lukáš

Commun. Math. 24, No. 1, 71-82 (2016).

This survey paper deals with the irrationality, transcendence algebraic and linear independence of infinite series and products consisting of rational numbers. The authors start with the Erdős method for the irrationality of infinite series and extend this to the expressible sets of sequences for sums and products.

Reviewer: Jaroslav Hančl (Ostrava)

MSC:

11J72	Irrationality; linear independence over a field
11J81	Transcendence (general theory)
11J85	Algebraic independence; Gel’fond’s method

Keywords:

irrationality; transcendence; linear independence; algebraic independence; expressible set of sequence