Divisor

About: Divisor is a research topic. Over the lifetime, 2462 publications have been published within this topic receiving 21394 citations. The topic is also known as: factor & submultiple.

On the distribution of integers with divisors in two consecutive intervals

Abstract: We investigate a new problem related to the multiplicative structure of integers. We introduce a new function H1, 1(x, y, z1, z2), the number of positive integers n ≤ x having exactly one divisor in interval (y, z1] and one in (z1, z2]. Our aim is to estimate its order of magnitude under some general conditions on y, z1 and z2.

Primitive divisors of elliptic divisibility sequences for elliptic curves with j=1728

Abstract: Take a rational elliptic curve defined by the equation $y^2=x^3+ax$ in minimal form and consider the sequence $B_n$ of the denominators of the abscissas of the iterate of a non-torsion point; we show that $B_{5m}$ has a primitive divisor for every $m$. Then, we show how to generalize this method to the terms in the form $B_{mp}$ with $p$ a prime congruent to $1$ modulo $4$.

An Algorithm to Factorize in a Quotient Ring

Abstract: The motivation for my study is that some examples of graded factorial rings dierent from the polynomial ring are known. Classical examples of varieties whose coordinate ring is a graded factorial domain include generic surfaces of P 3 with order m 4, non singular quadrics of P n (n 4), and Grassmannians are (see (No), (Na), and (Sa)). Moreover, it possible to construct more examples graded factorial domains taking A(X;D) = L n 0 H 0 (X;OX(nD))T n K(X)[T ] where X is an integral, normal, projective scheme dened over a eld K whose divisor class group is Cl(X) =Z, and D is a well dened

Moduli spaces of nonspecial pointed curves of arithmetic genus 1

Abstract: In this paper we study the moduli stack ${\mathcal U}_{1,n}^{ns}$ of curves of arithmetic genus 1 with n marked points, forming a nonspecial divisor. In arXiv:1511.03797 this stack was realized as the quotient of an explicit scheme $\widetilde{\mathcal U}_{1,n}^{ns}$, affine of finite type over ${\Bbb P}^{n-1}$, by the action of ${\Bbb G}_m^n$ . Our main result is an explicit description of the corresponding GIT semistable loci in $\widetilde{\mathcal U}_{1,n}^{ns}$. This allows us to identify some of the GIT quotients with some of the modular compactifications of ${\mathcal M}_{1,n}$ defined by Smyth in arXiv:0902.3690 and arXiv:0808.0177.

Prescribing Gaussian curvature on closed Riemann surface with conical singularity in the negative case

Abstract: The problem of prescribing Gaussian curvature on Riemann surface with conical singularity is considered. Let $(\Sigma,\beta)$ be a closed Riemann surface with a divisor $\beta$, and $K_\lambda=K+\lambda$, where $K:\Sigma\rightarrow\mathbb{R}$ is a Holder continuous function satisfying $\max_\Sigma K= 0$, $K ot\equiv 0$, and $\lambda\in\mathbb{R}$. If the Euler characteristic $\chi(\Sigma,\beta)$ is negative, then by a variational method, it is proved that there exists a constant $\lambda^\ast>0$ such that for any $\lambda\leq 0$, there is a unique conformal metric with the Gaussian curvature $K_\lambda$; for any $\lambda$, $0 \lambda^\ast$, there is no certain conformal metric having $K_{\lambda}$ its Gaussian curvature. This result is an analog of that of Ding and Liu \cite{Ding-Liu}, partly resembles that of Borer, Galimberti and Struwe \cite{B-G-Stru}, and generalizes that of Troyanov \cite{Troyanov} in the negative case.