Kirby-Melvin's ${\tau }_r^{{}^{\mathrm{\prime }}}$ and Ohtsuki's $\tau$ for Lens spaces

In this note, we first derive explicit formulas for Kirby-Melvin’s three-manifold invariants ${\tau }_r^{{}^{\mathrm{\prime }}}$ for all Lens spaces from our results for another set of invariants ${\xi }_r$ defined by the first author. Then, as a corollary, we obtain formulas for Othsuki’s $\tau$ for all Lens spaces.