Desingularization and p-Curvature of Recurrence Operators

Linear recurrence operators in characteristic $p$ are classified by their $p$-curvature. For a recurrence operator $L$, denote by $χ(L)$ the characteristic polynomial of its $p$-curvature. We can obtain information about the factorization of $L$ by factoring $χ(L)$. The main theorem of this paper gives an unexpected relation between $χ(L)$ and the true singularities of $L$. An application is to speed up a fast algorithm for computing $χ(L)$ by desingularizing $L$ first. Another contribution of this paper is faster desingularization.

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