On the p-adic Second Main Theorem
Complex Variables
2013-03-19 v1 Number Theory
Abstract
We study the Second Main Theorem in non-archimedean Nevanlinna theory, giving an improvement to the non-archimedean Second Main Theorems of Ru and An in the case where all the hypersurfaces have degree greater than one and all intersections are transverse. In particular, under a transversality assumption, if f is a nonconstant non-archimedean analytic map to P^n and D_1,..,D_q are hypersurfaces of degree d, we prove the defect relation \sum_{i=1}^q\delta_f(D_i)\leq n-1+1/d, which is sharp for all positive integers n and d.
Cite
@article{arxiv.1303.4122,
title = {On the p-adic Second Main Theorem},
author = {Aaron Levin},
journal= {arXiv preprint arXiv:1303.4122},
year = {2013}
}