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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc94-0-5,
author = {Alexandru Buium and Arnab Saha},
title = {Differential overconvergence},
journal = {Banach Center Publications},
volume = {95},
year = {2011},
pages = {99-129},
zbl = {1244.11059},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc94-0-5}
}
Alexandru Buium; Arnab Saha. Differential overconvergence. Banach Center Publications, Tome 95 (2011) pp. 99-129. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc94-0-5/