Differential Equations for Fq-Linear Functions
Anatoly N. Kochubei
Abstract
We study certain classes of equations for Fq-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 Fq-linear differential operators are also studied.
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