17 citations · 65 across the 14 of their papers we have counts for
14 papers · 1 filter
Liminal -representations and odd-th cyclic covers of genus one two-bridge knots
Honami Sakamoto, Ryoto Tange, Jun Ueki
Let be a prime number and let be a genus one two-bridge knot. In the spirit of arithmetic topology, we observe that if divides the size of the 1st homology group of som…
Multiplicity of non-acyclic -representations and L-functions of the odd-twisted Whitehead links
Léo Bénard, Ryoto Tange, Anh T. Tran +1
We study the divisor of the Reidemeister torsion on the variety of irreducible -characters of certain knots and links, and provide a geometric interpretation…
A Hilbert reciprocity law on 3-manifolds
Hirofumi Niibo, Jun Ueki
Based on our homological idelic class field theory, we formulate an analogue of the Hilbert reciprocity law on a rational homology 3-sphere endowed with an infinite link, in the sp…
Twisted Iwasawa invariants of knots
Ryoto Tange, Jun Ueki
Let be a prime number and an integer coprime to . In the spirit of arithmetic topology, we introduce the notions of the twisted Iwasawa invariants of ${\rm GL}…
Modular knots, automorphic forms, and the Rademacher symbols for triangle groups
Toshiki Matsusaka, Jun Ueki
É.Ghys proved that the linking numbers of modular knots and the "missing" trefoil in coincide with the values of a highly ubiquitous function called the Rademacher…
Modular knots obey the Chebotarev law
Jun Ueki
We study knots which behave like prime numbers. We discuss the planetary link raised from a hyperbolic fibered link in with an emphasis on surgeries, point out certain subtle…
Non-acyclic -representations of twist knots, -Dehn surgeries, and -functions
Ryoto Tange, Anh T. Tran, Jun Ueki
We study irreducible -representations of twist knots. We first determine all non-acyclic -representations, which turn out to lie on a line denot…
Profinite rigidity for twisted Alexander polynomials
Jun Ueki
We formulate and prove a profinite rigidity theorem for the twisted Alexander polynomials up to several types of finite ambiguity. We also establish torsion growth formulas of the…
Chebotarev links are stably generic
Jun Ueki
We discuss the relationship between two analogues in a 3-manifold of the set of prime ideals in a number field. We prove that if is a sequence of kno…
The profinite completions of knot groups determine the Alexander polynomials
Jun Ueki
We study several properties of the completed group ring and the completed Alexander modules of knots. Then we prove that if the p…
-adic Mahler measure and -covers of links
Jun Ueki
Let be a prime number. We develop a theory of -adic Mahler measure of polynomials and apply it to the study of -covers of rational homology 3-spheres branched ov…
On the Iwasawa invariants for links and Kida's formula
Jun Ueki
Analogues of Iwasawa invariants in the context of 3-dimensional topology have been studied by M.~Morishita and others. In this paper, following the dictionary of arithmetic topolog…
Idèlic class field theory for 3-manifolds and very admissible links
Hirofumi Niibo, Jun Ueki
We study a topological analogue of idèlic class field theory for 3-manifolds, in the spirit of arithmetic topology. We firstly introduce the notion of a very admissible link $\math…
On the universal deformations for SL_2-representations of knot groups
Masanori Morishita, Yu Takakura, Yuji Terashima +1
Based on the analogies between knot theory and number theory, we study a deformation theory for SL_2-representations of knot groups, following after Mazur's deformation theory of G…