On certain L-functions for deformations of knot group representations
Geometric Topology
2016-08-31 v3 Algebraic Topology
Number Theory
Abstract
We study the twisted knot module for the universal deformation of an -representation of a knot group, and introduce an associated -function, which may be seen as an analogue of the algebraic -adic -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 -function by some concrete examples for 2-bridge knots.
Cite
@article{arxiv.1506.00351,
title = {On certain L-functions for deformations of knot group representations},
author = {Takahiro Kitayama and Masanori Morishita and Ryoto Tange and Yuji Terashima},
journal= {arXiv preprint arXiv:1506.00351},
year = {2016}
}
Comments
35 pages, to appear in Transactions of the AMS. arXiv admin note: text overlap with arXiv:1409.4226