  We prove that some of the basic differential functions appearing in the
(unramified) theory of arithmetic differential equations, especially some of
the basic differential modular forms in that theory, arise from a "ramified
situation". This property can be viewed as a special kind of overconvergence
property. One can also go in the opposite direction by using differential
functions that arise in a ramified situation to construct "new" (unramified)
differential functions.
