Values of globally bounded G-functions

Abstract : 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).
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

Cited literature [17 references]  Display  Hide  Download
Contributor : Tanguy Rivoal <>
Submitted on : Tuesday, October 10, 2017 - 7:32:41 PM
Last modification on : Monday, December 3, 2018 - 7:24:49 AM
Long-term archiving on: Thursday, January 11, 2018 - 2:08:23 PM


Files produced by the author(s)


  • HAL Id : hal-01493550, version 2


S Fischler, Tanguy Rivoal. Values of globally bounded G-functions. 2017. ⟨hal-01493550v2⟩



Record views


Files downloads