F_q-线性函数的微分方程
Differential Equations for F_q-Linear Functions
摘要：
本文研究了$F_q$ -线性函数的某些类方程，它们是线性常微分方程的自然函数域对应。结果表明，与经典解和$p$ -adic解相比，形式幂级数解在方程的奇点附近具有正的收敛半径.研究了$F_q$ -线性微分算子环的代数性质。
英文摘要：
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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