A vanishing identity of adjoint Reidemeister torsions of twist knots

For a compact oriented 3-manifold with torus boundary the adjoint Reidemeister torsion is defined as function on $\mathrm{SL}_2(\mathbb{C})$-character variety depending choice of curve. Under reasonable assumptions, it conjectured that satisfies certain type vanishing identities. In this paper, we prove conjecture holds for all hyperbolic twist knot exteriors by using Jacobi's residue theorem.