# On the linear independence of values of G-functions

@article{Lepetit2021OnTL,
title={On the linear independence of values of G-functions},
author={Gabriel Lepetit},
journal={Journal of Number Theory},
year={2021},
volume={219},
pages={300-343}
}
• Gabriel Lepetit
• Published 1 February 2021
• Mathematics
• Journal of Number Theory
1 Citations
Quantitative problems on the size of G-operators
$G$-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

## References

SHOWING 1-10 OF 16 REFERENCES
Linear independence of values of G-functions, II: outside the disk of convergence
• Mathematics, Physics
• 2018
Given any non-polynomial G -function $$F(z)=\sum _{k=0}^\infty A_kz^k$$ F ( z ) = ∑ k = 0 ∞ A k z k of radius of convergence R and in the kernel a G -operator $$L_F$$ L F , we consider the G
Linear independence of linear forms in polylogarithms
For x ∈ C, |x | < 1, s ∈ N, let Lis(x) be the s-th polylogarithm of x . We prove that for any non-zero algebraic number α such that |α| < 1, the Q(α)-vector space spanned by 1, Li1(α), Li2(α), . . .
Quantitative problems on the size of G-operators
$G$-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
Séries Gevrey de type arithmétique, I. Théorèmes de pureté et de dualité
Gevrey series are ubiquitous in analysis; any series satisfying some (possibly non-linear) analytic differential equation is Gevrey of some rational order. The present work stems from two
Linear independence of values of $G$-functions
• Mathematics
• 2017
Given any non-polynomial $G$-function $F(z)=\sum\_{k=0}^\infty A\_k z^k$ of radius of convergence $R$, we consider the $G$-functions $F\_n^{[s]}(z)=\sum\_{k=0}^\infty \frac{A\_k}{(k+n)^s}z^k$ for any
ESTIMATES FROM BELOW OF POLYNOMIALS IN THE VALUES OF ANALYTIC FUNCTIONS OF A CERTAIN CLASS
Estimates from below are obtained for polynomials with integral coefficients in the values of certain Siegel -functions at the algebraic points of a special form. In particular, it is proved that if
TRANSCENDENTAL NUMBERS
The Greeks tried unsuccessfully to square the circle with a compass and straightedge. In the 19th century, Lindemann showed that this is impossible by demonstrating that π is not a root of any
Ordinary Differential Equations In The Complex Domain
Thank you very much for reading ordinary differential equations in the complex domain, maybe you have knowledge that, people have look hundreds of times for their chosen readings like this, but end up in infectious downloads.
Indépendance linéaire des valeurs des polylogarithmes
Nous montrons que pour tout rationnel a de [-1,1], l'ensemble des valeurs des polylogarithmes {Li,(a),s E N, s > 1} contient une infinite de nombres Q-lineairement independants.
Über einige Anwendungen diophantischer Approximationen
Die bekannte einfache Schlusweise, das bei einer Verteilung von mehr als n Dingen auf n Facher in mindestens einem Fach mindestens zwei Dinge gelegen sind, enthalt eine Verallgemeinerung des