Non-acyclic ${\mathrm{SL}}_2$-representations of twist knots, $-3$-Dehn surgeries, and $L$-functions

Ryoto Tange, Anh T. Tran, Jun Ueki

We study irreducible ${\mathrm{SL}}_2$-representations of twist knots. We first determine all non-acyclic ${\mathrm{SL}}_2(\mathbb{C})$-representations, which turn out to lie on a line denot…