Differential Equations for F_q-Linear Functions, by Anatoly N. Kochubei

We study certain classes of equations for $F_q$-linear functions, which are the natural function field counterparts of linear ordinary differential equations. It is shown that, in contrast to both classical and $p$-adic cases, formal power series solutions have positive radii of convergence near a singular point of an equation. Algebraic properties of the ring of $F_q$-linear differential operators are also studied.

Anatoly N. Kochubei <ank@ank.kiev.ua>