On certain $L$-functions for deformations of knot group representations
On certain $L$-functions for deformations of knot group representations
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关于结组表示变形的某些 $L$ 函数
DOI：
10.1090/tran/7037
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发表时间：
2017
影响因子：
1.3
通讯作者：
Terashima Yuji
中科院分区：
文献类型：
--
作者：
Kitayama Takahiro;Morishita Masanori;Tange Ryoto;Terashima Yuji
本文研究了纽结群的一个表示的泛变形的扭纽结模，并引入了一个伴随函数，它可以看作是与Galois表示的泛变形的塞尔默模相关联的代数进函数的一个类似.然后我们研究了Mazur提出的两个问题：第一，在一定条件下证明了泛变形环上扭纽结模的挠性质。其次，通过具体的例子计算了-桥结点的-函数。引用
We study the twisted knot module for the universal deformation of an-representation of a knot group and introduce an associated-function, which may be seen as an analogue of the algebraic-adic-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-function by some concrete examples for-bridge knots. References