42 citations · 260 across the 31 of their papers we have counts for
6 papers · 1 filter
Hypertranscendence and linear difference equations, the exponential case
Thomas Dreyfus
In this paper we study meromorphic functions solutions of linear shift difference equations in coefficients in involving the operator , for s…
On the computation of the difference Galois groups of order three equations
Thomas Dreyfus, Marina Poulet
In this paper we consider the problem of computing the difference Galois groups of order three equations for a large class of difference operators including the shift operator (Cas…
Algebraic independence and linear difference equations
Boris Adamczewski, Thomas Dreyfus, Charlotte Hardouin +1
We consider pairs of automorphisms acting on fields of Laurent or Puiseux series: pairs of shift operators , of -differ…
Hypertranscendence and linear difference equations
Boris Adamczewski, Thomas Dreyfus, Charlotte Hardouin
After Hölder proved his classical theorem about the Gamma function, there has been a whole bunch of results showing that solutions to linear difference equations tend to be hypertr…
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…
Functional relations of solutions of q-difference equations
Thomas Dreyfus, Charlotte Hardouin, Julien Roques
In this paper, we study the algebraic relations satisfied by the solutions of -difference equations and their transforms with respect to an auxiliary operator. Our main tool is…