Related papers: Division polynomials for twisted Edwards curves
In recent years, twisted Alexander polynomial has been playing an important role in low-dimensional topology. For Montesinos links, we develop an efficient method to compute the twisted Alexander polynomial associated to any linear…
In this paper, we gave some properties of binomial coefficient.
We classify all geometric torsion points on the Fermat quotients $y^n = x^d + 1$ where $n, d \ge 2$ are coprime. In addition, we classify all geometric torsion points on the generic superelliptic curve $y^n = (x - a_1) \cdots (x - a_d)$,…
The Alexander polynomial of a knot has been generalized in three different ways to give twisted invariants. The resulting invariants are usually referred to as twisted Alexander polynomials, higher-order Alexander polynomials and…
We define and study twisted Alexander-type invariants of complex hypersurface complements. We investigate torsion properties for the twisted Alexander modules and extend classical local-to-global divisibility results to the twisted setting.…
In this paper, we consider a family of twists of a superelliptic curve over a global field, and obtain results on the distribution of the Mordell-Weil rank of these twists. Our results have applications to the distribution of the number of…
In this paper, we study properties of polynomials over division rings. Moreover, we present formulas for finding roots of some polynomials
We use Reidemeister torsion to study a twisted Alexander polynomial, as defined by Turaev, for links in the projective space. Using sign-refined torsion we derive a skein relation for a normalized form of this polynomial.
In order to give a formal treatment of differential equations in positive characteristic p, it is necessary to use divided powers. One runs into an analog problem in the theory of q-difference equations when q is a pth root of unity. We…
Let $\mathbb{F}_q$ be a finite field with $q$ elements. For $a,b,c,d,e,f \in \mathbb{F}_q^{\times}$, denote by $C_{a,b,c,d,e,f}$ the family of algebraic curves over $\mathbb{F}_q$ given by the affine equation \begin{align*}…
We give explicit formulas for the adjoint twisted Alexander polynomial and the nonabelian Reidemeister torsion of genus one two-bridge knots.
We start with $n$-torsions in the Jacobian of an $m$-gonal curve and produce $n$-torsions in the class group of certain number field $K$.
As a generalization of a fundamental result about the Alexander polynomial of links, we give a description of a Torres condition for the twisted Alexander polynomial of links associated to a unimodular representation.
We give an efficient algorithm to compute equations of twists of hyperelliptic curves of arbitrary genus over any separable field (of characteristic different from 2), and we explicitly describe some interesting examples.
Consider degenerations of Abelian differentials with prescribed number and multiplicity of zeros and poles. Motivated by the theory of limit linear series, we define twisted canonical divisors on pointed nodal curves to study degenerate…
We extend our method to compute division polynomials of Jacobians of curves over Q to curves over Q(t), in view of computing mod ell Galois representations occurring in the \'etale cohomology of surfaces over Q. Although the division…
In this paper, we will constructed p-adic twisted q-l-functions which is a part of answer of the question in [8]. Finally, we will treat many interesting properties related to twisted q-Euler numbers and polynomials.
We provide the twisted Alexander polynomials of finite abelian covers over three-dimensional manifolds whose boundary is a finite union of tori. This is a generalization of a well-known formula for the usual Alexander polynomial of knots in…
We introduce a new notion of generalized log twisted curves, which are marked nodal curves with additional data at the marked points. In the case when the markings are distinct this notion agrees with the notion of twisted curve introduced…
Twisted links are obtained from a base link by starting with a $n$-braid representation, choosing several ($m$) adjacent strands, and applying one or more twists to the set. Various restrictions may be applied, e.g. the twists may be…