On certain L-functions for deformations of knot group representations

Abstract

We study the twisted knot module for the universal deformation of an ${\mathrm{SL}}_2$-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.

35 pages, to appear in Transactions of the AMS. arXiv admin note: text overlap with arXiv:1409.4226

References in corpus (1)

• On the universal deformations for SL_2-representations of knot groups

Cited by in corpus (2)

• The profinite completions of knot groups determine the Alexander polynomials
• Multiplicity of non-acyclic ${\mathrm{SL}}_2$-representations and L-functions of the odd-twisted Whitehead links