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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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Journal ArticleDOI
TL;DR: In this paper, a mean value of the additive divisor problem was studied and an upper bound for the case where the main term is the one given by Motohashi [27] was shown.
Posted Content
TL;DR: For irreducible divisors from the linear system, the Lagrangian shadows are Gelfand - Zeytlin type lagrangian 3 - spheres as discussed by the authors.
Abstract: In the framework of Special Bohr - Sommerfeld geometry it was established that an ample divisor in compact algebraic variety can define almost canonically certain real submanifold which is lagrangian with respect to the corresponding Kahler form. It is natural to call it "lagrangian shadow"; below we emphasize this correspondence and present some simple examples, old and new. In particular we show that for irreducible divisors from the linear system $\vert - \frac{1}{2} K_{F^3} \vert$ on the full flag variety $F^3$ their lagrangian shadows are Gelfand - Zeytlin type lagrangian 3 - spheres.
Patent
16 Oct 2007
TL;DR: In this article, a clock-generating circuit with one or more clock-processing circuits, each outputting a clock signal having an adjustable phase, is presented. But the authors do not specify the phase of the corresponding output clock signal.
Abstract: In one embodiment, the invention can be a clock-generating circuit having one or more clock-processing circuits, each outputting a clock signal having an adjustable phase. Each clock-processing circuit comprises a divider and a divisor control circuit. Each divider divides an input clock signal by a respective divisor value and outputs a corresponding output clock signal whose period is determined by the divisor value and the period of the input clock signal. Each divider receives the respective divisor value from the corresponding divisor control circuit, wherein the divisor value is selected in order to achieve a desired frequency and phase for the corresponding output clock signal. Temporarily changing a divisor value can advance or delay the phase of the corresponding output clock signal without having to reset the divider.
Posted Content
TL;DR: In this article, it was shown that minimal models of NQC log canonical generalised pairs with smooth models of smooth varieties exist, assuming the existence of minimal models for smooth varieties.
Abstract: We show that minimal models of $\mathbb{Q}$-factorial NQC log canonical generalised pairs exist, assuming the existence of minimal models of smooth varieties. More generally, we prove that on a $\mathbb{Q}$-factorial NQC log canonical generalised pair $ (X,B+M) $ we can run an MMP with scaling of an ample divisor which terminates, assuming that it admits an NQC weak Zariski decomposition or that $ K_X+B+M$ is not pseudoeffective. As a consequence, we establish several existence results for minimal models and Mori fibre spaces in dimensions at most $ 5 $.
Posted Content
TL;DR: In this paper, it was shown that all modular units on the positive integer X_0(N) can be written as products of generalized Dedekind eta functions, and the necessary and sufficient conditions for such products to be modular units under a mild assumption.
Abstract: For a positive integer $N$, let $\mathscr{C}_N(\mathbb{Q})$ be the rational cuspidal subgroup of $J_0(N)$ and $\mathscr{C}(N)$ be the rational cuspidal divisor class group of $X_0(N)$, which are both subgroups of the rational torsion subgroup of $J_0(N)$. We prove that two groups $\mathscr{C}_N(\mathbb{Q})$ and $\mathscr{C}(N)$ are equal when $N=p^2M$ for any prime $p$ and any squarefree integer $M$. To achieve this we show that all modular units on $X_0(N)$ can be written as products of certain functions $F_{m, h}$, which are constructed from generalized Dedekind eta functions. Also, we determine the necessary and sufficient conditions for such products to be modular units on $X_0(N)$ under a mild assumption.

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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20222
2021157
2020172
2019127
2018120
2017140