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arXiv · 2111.08917

Non-Archimedean second main theorem sharing small functions

Ta Thi Hoai An·Nguyen Viet Phuong
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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 $q\, (q\geq 5)$ 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}.

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Ta Thi Hoai An, Nguyen Viet Phuong. 2021-11-17. Non-Archimedean second main theorem sharing small functions. https://arxiv.org/abs/2111.08917

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