Let $X$ be a Riemann surface and let $p\in X$. Let: $$\text{Res}_p:\Omega^1_{\text{mero}}(X)\to \mathbb{C}$$ be the residue at $p$ operator defined on meromorphic $1$-forms. Clearly holomorphic $1$-forms are in the kernel of this operator. By Stokes theorem also differentials of meromorphic functions are in the kernel.
Is this a complete description of the kernel?
In other words , does the following equality hold?
$$\text{ker}(\text{Res}_p)=\Omega^1(X)+d\mathscr{M}(X)$$