Non-Archimedean second main theorem sharing small functions

2021/11/17 by An, Ta Thi Hoai, Phuong, Nguyen Viet
#Complex Variables (math.CV) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2111.08917

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≥ 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 \citeEY.

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