13 citations · 31 across the 10 of their papers we have counts for
10 papers
The Carlitz module and a differential Ax-Lindemann-Weierstrass theorem for the Euler gamma function
Lucia Di Vizio, Federico Pellarin
We prove a differential transcendence result of type "Ax-Lindemann-Weierstrass" for Euler's gamma function. Given meromorphic functions of a complex variable th…
Singular walks in the quarter plane and Bernoulli numbers
Alin Bostan, Lucia Di Vizio, Kilian Raschel
We consider singular (aka genus ) walks in the quarter plane and their associated generating functions , which enumerate the walks starting from the origin, of fixed e…
Inhomogeneous order 1 iterative functional equations with applications to combinatorics
Lucia Di Vizio, Gwladys Fernandes, Marni Mishna
We show that if a Laurent series satisfies a particular kind of linear iterative equation, then is either a rational function or it is differentially tran…
A Galoisian proof of Ritt theorem on the differential transcendence of Poincaré functions
Lucia Di Vizio, Gwladys Fernandes
Using Galois theory of functional equations, we give a new proof of the main result of the paper "Transcendental transcendency of certain functions of Poincaré" by J.F. Ritt, on th…
Reduced Forms of Linear Differential Systems and the Intrinsic Galois-Lie Algebra of Katz
Moulay Barkatou, Thomas Cluzeau, Lucia Di Vizio +1
Generalizing the main result of [Aparicio-Monforte A., Compoint E., Weil J.-A., J. Pure Appl. Algebra 217 (2013), 1504-1516], we prove that a linear differential system is in reduc…
Local analytic classification of -difference equations with
Lucia Di Vizio
In this paper, we establish, under convenient diophantine assumptions, a complete analytic classification of -difference modules over the field of germs of meromorphic functions…