On the genus of meromorphic functions

We define the class of Left Located Divisor (LLD) meromorphic functions and their vertical order $m_0(f)$ and their convergence exponent $d(f)$. When $m_0(f)\le d(f)$ we prove that their Weierstrass genus is minimal. This explains the phenomena that many classical functions have minimal Weierstrass genus, for example Dirichlet series, the $\mathrm{\Gamma }$-function, and trigonometric functions.