# Quantitative problems on the size of G-operators

@article{Lepetit2021QuantitativePO,
title={Quantitative problems on the size of G-operators},
author={Gabriel Lepetit},
journal={manuscripta mathematica},
year={2021}
}
$G$-operators, a class of differential operators containing the differential operators of minimal order annihilating Siegel's $G$-functions, satisfy a condition of moderate growth called Galochkin condition, encoded by a $p$-adic quantity, the size. Previous works of Chudnovsky, Andre and Dwork have provided inequalities between the size of a $G$ -operator and certain computable constants depending among others on its solutions. First, we recall Andre's idea to attach a notion of size to… Expand
2 Citations
On the linear independence of values of G-functions
Abstract We consider a G-function F ( z ) = ∑ k = 0 ∞ A k z k ∈ K 〚 z 〛 , where K is a number field, of radius of convergence R and annihilated by the G-operator L ∈ K ( z ) [ d / d z ] , and aExpand
A note on G-operators of order 2
• Mathematics
• 2021
It is known that G-functions solutions of a linear differential equation of order 1 with coefficients in Q(z) are algebraic (of a very precise form). No general result is known when the order is 2.Expand

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