Abstract

In this paper, we show that two admissible meromorphic functions on an annulus must coincide to each other if they share q (q≥5) distinct small functions regardless of multiplicity. We also show that such two meromorphic functions must be linked by a quasi-Möbius transformation if they share four distinct small functions with multiplicities truncated by a certain level. Moreover, in our result, all intersection points of such meromorphic functions with small functions do not need to be counted if their multiplicities are bigger than a certain number.