Differential Equations for F_q-Linear Functions

Details Differential Equations for F_q-Linear Functions Differential Equations for F_q-Linear Functions

1999-11-11

arxiv.org/abs/math/9911075v1

Mathematics

Number Theory

17 pages, LaTex-2e

Scientific paper

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.

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