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.
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24 Oct 1988
TL;DR: In this paper, an Omega lower bound on the depth of any computation tree with operations (+, -, /, mod, >) was proved, and a lower bound of O(log log n) was also proved.
Abstract: An Omega (log log n) lower bound is proved on the depth of any computation tree with operations (+, -, /, mod, >
13 citations
Posted Content•
TL;DR: In this paper, the authors studied sums of the shape of the von Mangoldt function and Dirichlet-Piltz divisor function with respect to the von Mabrouk function.
Abstract: We study sums of the shape $\sum_{n \leqslant x} f \left( \lfloor x/n \rfloor \right)$ where $f$ is either the von Mangoldt function or the Dirichlet-Piltz divisor functions. We improve previous estimates when $f = \Lambda$ and $f = \tau$, and provide new results when $f = \tau_r$ with $r \geqslant 3$, breaking the $\frac{1}{2}$-barrier in each case. The functions $f=\mu^2$, $f=2^\omega$ and $f=\omega$ are also investigated.
13 citations
Patent•
15 Mar 1971
TL;DR: In this article, a method and apparatus for performing division by selecting a trial quotient digit from a table derived from a consideration of only the leading digits of the dividend and divisor is presented.
Abstract: A method and apparatus for performing division by selecting a trial quotient digit from a table derived from a consideration of only the leading digits of the dividend and divisor. The trial quotient digit is the maximum of a restricted range of possible quotient digits and is used to select a corresponding multiple of the divisor which is then tested by subtraction from the dividend. The trial quotient digit is subsequently adjusted if necessary. A basic apparatus and a computer program is also described to illustrate the implementation of the method by means of a digital computer. A table look-up procedure for obtaining the multiples of the divisor may also be used in a method of multiplication.
13 citations
TL;DR: In this article, a rational Remmert reduction for the universal cover of smooth orbifolds (X/Δ) is presented, and some singular Kahler metrics adapted to the \(mathbb {Q}) -divisor Δ are introduced.
Abstract: The aim of this short note is to show how to construct a rational Remmert reduction (the \({\widetilde \Gamma}\) -reduction) for the universal cover of smooth orbifolds (X/Δ). Doing this, we are led to introduce some singular Kahler metrics on (X/Δ) adapted to the \({\mathbb {Q}}\) -divisor Δ.
13 citations
TL;DR: In this article, an infinite family of irreducible homogeneous free divisors in K[x, y, z] is constructed, and the set of monomials X such that the general polynomial supported on X is a non-free divisor is identified.
Abstract: An infinite family of irreducible homogeneous free divisors in K[x, y, z] is constructed. Indeed, we identify sets of monomials X such that the general polynomial supported on X is a free divisor.
13 citations