Topic
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.
Papers published on a yearly basis
Papers
More filters
Posted Content•
TL;DR: In this paper, the authors studied the problem of obtaining asymptotic formulas for the sums of the von Mangoldt function and the divisor function, where the sum is the sum of all the sums.
Abstract: We study the problem of obtaining asymptotic formulas for the sums $\sum_{X < n \leq 2X} d_k(n) d_l(n+h)$ and $\sum_{X < n \leq 2X} \Lambda(n) d_k(n+h)$, where $\Lambda$ is the von Mangoldt function, $d_k$ is the $k^{\operatorname{th}}$ divisor function, $X$ is large and $k \geq l \geq 2$ are real numbers. We show that for almost all $h \in [-H, H]$ with $H = (\log X)^{10000 k \log k}$, the expected asymptotic estimate holds. In our previous paper we were able to deal also with the case of $\Lambda(n) \Lambda(n + h)$ and we obtained better estimates for the error terms at the price of having to take $H = X^{8/33 + \varepsilon}$.
Posted Content•
TL;DR: In this article, it was shown that every unit of R is an involution if and only of n is a divisor of 12 in the ring of polynomials in finitely many commuting variables with coefficients in Z n.
Abstract: Let R be the ring of polynomials in finitely many commuting variables with coefficients in Z_n. It is shown that every unit of R is an involution if and only of n is a divisor of 12.
Posted Content•
TL;DR: In this paper, the number of automorphisms of a prime number fixing elements of a divisor of a given prime number was shown to be Ω(G,d).
Abstract: Let $G=\mathbf{Z}_{p} \oplus \mathbf{Z}_{p^2}$ where $p$ is a prime number. Suppose that $d$ is a divisor of $G$. In this paper we find the number of automorphisms of $G$ fixing $d$ elements of $G$, and denote it by $\theta(G,d)$. As a consequence, we prove Conjecture $1$ of [2].
Posted Content•
03 Dec 2008
TL;DR: The GIT cone as mentioned in this paper, which is generated by the pullbacks of the natural ample line bundles on the GIT quotient, was introduced and studied in the context of weighted curves.
Abstract: We introduce and study the GIT CONE of $\bar{M}_{0,n}$, which is generated by the pullbacks of the natural ample line bundles on the GIT quotients $(\mathbb P^1)^n//SL(2)$. We give an explicit formula for these line bundles and prove a number of basic results about the GIT cone. As one application, we prove unconditionally that the log canonical models of $\bar{M}_{0,n}$ with a symmetric boundary divisor coincide with the moduli spaces of weighted curves or with the symmetric GIT quotient, extending the result of Matt Simpson arXiv:0709.4037. (Cf. also a different proof by Fedorchuk and Smyth arXiv:0810.1677)
Patent•
07 Sep 2017TL;DR: In this paper, the arithmetic unit stores a recurrence relation of the sequence and iteratively computes a quotient using the recurrence relations according to the plurality of initial parameters, which includes an initial term, a first term and a common ratio having an absolute value smaller than 1.
Abstract: Provided is a fast divider including an initial parameter setting unit and an arithmetic unit. The arithmetic unit is coupled to the initial parameter setting unit that receives a divisor and a dividend, and sets a plurality of initial parameters of a sequence according to the divisor and the dividend. The plurality of initial parameters includes an initial term, a first term and a common ratio having an absolute value smaller than 1. The arithmetic unit stores a recurrence relation of the sequence and iteratively computes a quotient using the recurrence relation according to the plurality of initial parameters. The recurrence relation indicates that a (k+1)th term is equal to a product of a kth term multiplied by a sum of the common ratio and 1 subtracted by a product of a (k−1)th term multiplied by the common ratio. k is an integer larger than or equal to 1.