On the value distribution of general Dirichlet series

We estimate the number of zeros and poles of $L-\alpha $, where $L$ is a general Dirichlet series satisfying some conditions and $\alpha $ is a meromorphic function with $T(r,\alpha )=o(r)$ as $r\rightarrow \infty $. In addition, we give a uniqueness theorem in terms of $a$-points of Dirichlet series and find Picard exceptional values of some Dirichlet series, which is an improvement of a theorem from B. Li [Quart. J. Math. 72 (2021), 1089–1097].