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Authors: Jaroslav Hančl, Katarína Korčeková and Lukáš Novotný

We introduce the two new concepts, productly linearly independent sequences and productly irrational sequences. Then we prove a criterion for which certain infinite sequences of rational numbers are productly linearly independent. As a consequence we obtain a criterion for the irrationality of infinite products and a criterion for a sequence to be productly irrational.

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Let {F n}n≥0 be the sequence of Fibonacci numbers. The aim of this paper is to give linear independence results over (5) for the infinite series n=1χj(n)/Fn with certain nonprincipal real Dirichlet characters χ j. We also deduce the irrationality results for the special principal Dirichlet characters and for other multiplicative functions.

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