2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/102128We provide a Mahler/Elkies-style lower bound for the average values of dynamical Green's functions on the projective line over an arbitrary valued field, and give some dynamical and arithmetic applications.15 pages; to appear in Mathematical Research Letters. Removed remark following Lemma 3.1Number TheoryDynamical Systemstext