We design a fast algorithm that computes, for a given linear differential operator with coefficients in $Z[x ]$, all the characteristic polynomials of its p-curvatures, for all primes $p < N$ , in asymptotically quasi-linear bit complexity in N. We discuss implementations and applications of our algorithm. We shall see in particular that the good performances of our algorithm are quickly visible.

翻译：我们设计了一种快速算法，该算法对于系数属于$Z[x]$的给定线性微分算子，能计算其所有素数$p < N$对应的p-曲率特征多项式，且渐近位复杂度在N上呈拟线性。文中讨论了该算法的实现与应用，特别指出其优异性能可快速显现。