Arithmetic properties of lacunary power series with integral coefficients

K. Mahler

doi:10.1017/S1446788700025866

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This note is concerned with arithmetic properties of power series with integral coefficients that are lacunary in the following sense. There are two infinite sequences of integers {rn} and {sn}, satisfying such that It is also assumed that f(z) has a positive radius of convergence, Rf say, where naturally . A power series with these properties will be called admissible.

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Arithmetic properties of lacunary power series with integral coefficients

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