Writhe polynomial for virtual links

A weak chord index $In{d}^{\mathrm{\prime }}$ is constructed for self crossing points of virtual links. Then a new writhe polynomial $W$ of virtual links is defined by using $In{d}^{\mathrm{\prime }}$. $W$ is a generalization of writhe polynomial defined in [6]. Based on $W$, three invariants of virtual links are constructed. These invariants can be used to detect the non-trivialities of Kishino knot and flat Kishino knot.