  We study the twisted knot module for the universal deformation of an ${\rm
SL}_2$-representation of a knot group, and introduce an associated
$L$-function, which may be seen as an analogue of the algebraic $p$-adic
$L$-function associated to the Selmer module for the universal deformation of a
Galois representation. We then investigate two problems proposed by Mazur:
Firstly we show the torsion property of the twisted knot module over the
universal deformation ring under certain conditions. Secondly we verify the
simplicity of the zeroes of the $L$-function by some concrete examples for
2-bridge knots.
