Geodesic
Diophantine Approximations of Infinite Series and Products
Communications in Mathematics, Tome 24 (2016) no. 1, pp. 71-82.

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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.
Classification : 11J72, 11J81, 11K55
Keywords: Infinite products; irrationality; linear independence; expressible set 
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     title = {Diophantine {Approximations} of {Infinite} {Series} and {Products}},
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Kolouch, Ondřej; Novotný, Lukáš. Diophantine Approximations of Infinite Series and Products. Communications in Mathematics, Tome 24 (2016) no. 1, pp. 71-82. http://geodesic.mathdoc.fr/item/COMIM_2016__24_1_a5/