## A criterion for linear independence of infinite products.(English)Zbl 1349.11105

Summary: Using an idea of Erd\'’ os 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.

### MSC:

 11J72 Irrationality; linear independence over a field

### Keywords:

linear independence; infinite product; irrationality