Non-Archimedean second main theorem sharing small functions

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 $1.$ As an application, we show that two meromorphic functions on a non-Archimedean field must coincide to each other if they share $q(q\ge 5)$ distinct small functions ignoring multiplicities. In particular, if two non-Archimedean meromorphic functions share $5$ small functions ignoring multiplicities, they must be identical. Thus, our work improves the results in \cite{EY}.