Arithmetical Results on Certain Multivariate Power Series

Power series with non-zero convergence radius R(f) are considered, and the arithmeticalnature (that is, irrationality, or even transcendence) of thecorresponding multivariate series is studied if x₁, ..., x_m and the sequence (f(n)) satisfy appropriatearithmetical conditions. It follows that such arithmetical resultscan be written down easily if linear independence results onthe function F(x), defined in |x| < R(f) by the originalone-dimensional power series, and possibly its derivatives atthe points x_µ are known. Some typical applications areexplicitly stated. 2000 Mathematics Subject Classification 11J72.