VALUES OF GLOBALLY BOUNDED G-FUNCTIONS.

In this paper we define and study a filtration (Gs)s≥0 on the algebra of values at algebraic points of analytic continuations of G-functions: Gs is the set of values at algebraic points in the disk of convergence of all Gfunctions Σ∞n=0 anzn for which there exist some positive integers b and c such that dsbncn+1an is an algebraic integer for any n, where dn = lcm(1, 2, . . ., n). We study the situation at the boundary of the disk of convergence, and using transfer results from analysis of singularities we deduce that constants in Gs appear in the asymptotic expansion of such a sequence (an). [ABSTRACT FROM AUTHOR]