On certain L-functions for deformations of knot group representations

Autor:	Kitayama, Takahiro, Morishita, Masanori, Tange, Ryoto, Terashima, Yuji
Rok vydání:	2015
Předmět:	Mathematics - Geometric Topology Mathematics - Algebraic Topology Mathematics - Number Theory 57M25
Druh dokumentu:	Working Paper
Popis:	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. Comment: 35 pages, to appear in Transactions of the AMS. arXiv admin note: text overlap with arXiv:1409.4226
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1506.00351 Zobrazit plný text záznamu View this record from Arxiv