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 SL2 -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 compute the L-function by some concrete examples for 2-bridge knots.

Original languageEnglish
Pages (from-to)3171-3195
Number of pages25
JournalTransactions of the American Mathematical Society
Volume370
Issue number5
DOIs
Publication statusPublished - May 2018

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All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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