Geodesic
On linear independence of values of certain $q$-series
Izvestiya. Mathematics , Tome 75 (2011) no. 1, pp. 177-221

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We obtain qualitative and quantitative results on the linear independence of the values of functions in a fairly wide class generalizing $q$-hypergeometric series and of their derivatives at algebraic points. The results are proved in both the Archimedean and $p$-adic cases.
Keywords: algebraic number field, absolute height of an algebraic number, $q$-series, $q$-exponential function, linear independence, linear independence measure, Hankel determinant
Mots-clés : $q$-logarithm, cyclotomic polynomial. 
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     author = {I. P. Rochev},
     title = {On linear independence of values of certain $q$-series},
     journal = {Izvestiya. Mathematics },
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     number = {1},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2011_75_1_a6/}
}
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I. P. Rochev. On linear independence of values of certain $q$-series. Izvestiya. Mathematics , Tome 75 (2011) no. 1, pp. 177-221. http://geodesic.mathdoc.fr/item/IM2_2011_75_1_a6/