1. On certain ๐ฟ-functions for deformations of knot group representations
- Author
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Yuji Terashima, Takahiro Kitayama, Ryoto Tange, and Masanori Morishita
- Subjects
Pure mathematics ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,MathematicsofComputing_GENERAL ,Galois module ,01 natural sciences ,Knot (unit) ,Knot group ,0103 physical sciences ,010307 mathematical physics ,0101 mathematics ,Algebraic number ,Mathematics - Abstract
We study the twisted knot module for the universal deformation of an SL 2 \textrm {SL}_2 -representation of a knot group and introduce an associated L L -function, which may be seen as an analogue of the algebraic p p -adic L 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 L -function by some concrete examples for 2 2 -bridge knots.
- Published
- 2017
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