On the rationality and continuity of logarithmic growth filtration of solutions of p-adic differential equations

Abstract

We study the asymptotic behavior of solutions of Frobenius equations defined over the ring of overconvergent series. As an application, we prove Chiarellotto–Tsuzuki's conjecture on the rationality and right continuity of Dwork's logarithmic growth filtrations associated to ordinary linear p-adic differential equations with Frobenius structures.