42 citations · 117 across the 11 of their papers we have counts for
12 papers
Frobenius method for Mahler equations
Julien Roques
Using Hahn series, one can attach to any linear Mahler equation a basis of solutions at 0 reminiscent of the solutions of linear differential equations at a regular singularity. We…
Algebraic solutions of linear differential equations: an arithmetic approach
Alin Bostan, Xavier Caruso, Julien Roques
Given a linear differential equation with coefficients in , an important question is to know whether its full space of solutions consists of algebraic functions, or…
On the algebraic dependence of holonomic functions
Julien Roques, Michael F. Singer
We study the form of possible algebraic relations between functions satisfying linear differential equations. In particular , if f and g satisfy linear differential equations and a…
On the Kernel curves associated with walks in the quarter plane
Thomas Dreyfus, Charlotte Hardouin, Julien Roques +1
The kernel method is an essential tool for the study of generating series of walks in the quarter plane. This method involves equating to zero a certain polynomial, the kernel poly…
Differential transcendence criteria for second-order linear difference equations and elliptic hypergeometric functions
Carlos E. Arreche, Thomas Dreyfus, Julien Roques
We develop general criteria that ensure that any non-zero solution of a given second-order difference equation is differentially transcendental, which apply uniformly in particular…
On the nature of the generating series of walks in the quarter plane
Thomas Dreyfus, Charlotte Hardouin, Julien Roques +1
In the present paper, we introduce a new approach, relying on the Galois theory of difference equations, to study the nature of the generating series of walks in the quarter plane.…