# 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…

## 2 Citations

On the linear independence of values of G-functions

- Mathematics
- 2021

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 a…

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.…

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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 a…

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