On consistent systems of linear differential and q-difference equations

par M. Youssef Yjjou

lundi 23 févr. 2026, 10:30 → 11:25 Europe/Paris

Fokko du Cloux (ICJ)

In 1992, J.-P. Ramis studied power series that satisfy both a linear differential equation and a q-difference equation simultaneously. He proved that such a constraint implies that the solution is necessarily a rational function. This result was then shown by R. Schäfke and M.F. Singer in 2017 through the study of a consistent system of linear differential and linear q-difference equations. By analysing the singularities and the monodromy of the system, they managed to prove that it is rationally equivalent to a much simpler system with constant coefficients. In this talk, I'll present some generalisations of these results to functions of several variables.