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Article Dans Une Revue Proceedings of the American Mathematical Society Année : 2019

Values of globally bounded G-functions

Tanguy Rivoal

Résumé

In this paper we define and study a filtration (G_s) on the algebra of values at algebraic points of analytic continuations of G-functions: G_s is the set of values at algebraic points in the disk of convergence of all G-functions sum_n a_n z^n for which there exist some positive integers b and c such that d_{s b}^n c^{n+1} a_n is an algebraic integer for any n, where d_n = 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 G_s appear in the asymptotic expansion of such a sequence (a_n).
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Dates et versions

hal-01493550 , version 1 (21-03-2017)
hal-01493550 , version 2 (10-10-2017)
hal-01493550 , version 3 (26-11-2018)

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S Fischler, Tanguy Rivoal. Values of globally bounded G-functions. Proceedings of the American Mathematical Society, 2019, ⟨10.1090/proc/14402⟩. ⟨hal-01493550v3⟩
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