The error term in Nevanlinna's second fundamental theorem for holomorphic mappings on coverings

摘要

We study the error term in Nevanlinna's second fundamental theorem for holomorphic mappings F : Y → P~1. where on Y is defined an holomorphic covering map p : Y → C. as considered by S.Lang and W.Cherry. We also obtain the logarithmic derivative lemma for this class of functions which, in particular, contains the class of algebroid functions. We show that our estimate improves a classical result of Henrik Selberg on the logarithmic derivative for algebroid functions.