A Non-Archimedean Second Main Theorem for Small Functions and Applications

We establish a slowly moving target second main theorem for meromorphic functions on a non-Archimedean field, with counting functions truncated to level 1. As an application, we show that two meromorphic functions on a non-Archimedean field must coincide if they share q (q > 5) distinct small functions, ignoring multiplicities. Thus, our work improves the results in [2].

Automated summary

We establish a slowly moving target second main theorem for meromorphic functions on a non-Archimedean field, with counting functions truncated to level 1. As an application, we show that two meromorphic functions on a non-Archimedean field must coincide if they share q (q > 5) distinct small functions, ignoring multiplicities. Thus, our work improves the results in [2].