Non-Archimedean second main theorem sharing small functions
Complex Variables
2021-12-28 v2 Number Theory
Abstract
In this paper, we establish a new second main theorem for meromorphic functions on a non-Archimedean field and small functions with counting functions truncated to level As an application, we show that two meromorphic functions on a non-Archimedean field must coincide to each other if they share distinct small functions ignoring multiplicities. In particular, if two non-Archimedean meromorphic functions share small functions ignoring multiplicities, they must be identical. Thus, our work improves the results in \cite{EY}.
Cite
@article{arxiv.2111.08917,
title = {Non-Archimedean second main theorem sharing small functions},
author = {Ta Thi Hoai An and Nguyen Viet Phuong},
journal= {arXiv preprint arXiv:2111.08917},
year = {2021}
}