On certain L-functions for deformations of knot group representations

Takahiro Kitayama; Masanori Morishita; Ryoto Tange; Yuji Terashima

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arXiv · 1506.00351

On certain L-functions for deformations of knot group representations

Takahiro Kitayama·Masanori Morishita·Ryoto Tange·Yuji Terashima

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Abstract

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.

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BibTeX RIS

Takahiro Kitayama, Masanori Morishita, Ryoto Tange, Yuji Terashima. 2016-08-30. On certain L-functions for deformations of knot group representations. https://arxiv.org/abs/1506.00351

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