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

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