@article{63d2a3dfebd4434c957c180e2b122ecf,

title = "On certain l-functions for deformations of knot group representations",

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.",

keywords = "Character schemes, Deformations of representations, L-functions, Twisted Alexander invariants, Twisted knot modules",

author = "Takahiro Kitayama and Masanori Morishita and Ryoto Tange and Yuji Terashima",

note = "Funding Information: Received by the editors December 17, 2015, and, in revised form, February 8, 2016 and July 22, 2016. 2010 Mathematics Subject Classification. Primary 57M25. Key words and phrases. Deformations of representations, character schemes, twisted knot modules, twisted Alexander invariants, L-functions. The first author was partly supported by JSPS Research Fellowships for Young Scientists 26800032. The second author was partly supported by Grants-in-Aid for Scientific Research (B) 24340005. The fourth author was partly supported by Grants-in-Aid for Scientific Research (C) 25400083. Publisher Copyright: {\textcopyright} 2017 American Mathematical Society.",

year = "2018",

month = may,

doi = "10.1090/tran/7037",

language = "English",

volume = "370",

pages = "3171--3195",

journal = "Transactions of the American Mathematical Society",

issn = "0002-9947",

publisher = "American Mathematical Society",

number = "5",

}