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Ondřej Kolouch and Lukáš Novotný

Abstract

This survey paper presents some old and new results in Diophantine approximations. Some of these results improve Erdos’ results on irrationality. The results in irrationality, transcendence and linear independence of infinite series and infinite products are put together with idea of irrational sequences and expressible sets.

Open access

Jaroslav Hančl, Ondřej Kolouch and Lukáš Novotný

Abstract

Using an idea of Erdős the paper establishes a criterion for the linear independence of infinite products which consist of rational numbers. A criterion for irrationality is obtained as a consequence.