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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.


Papers
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Journal ArticleDOI
TL;DR: In this paper, the authors investigated the behavior of the divisor function in both short intervals and in arithmetic progressions, and they proved a complementary result to their main theorem.
Abstract: We investigate the behavior of the divisor function in both short intervals and in arithmetic progressions. The latter problem was recently studied by E. Fouvry, S. Ganguly, E. Kowalski, and Ph. Michel. We prove a complementary result to their main theorem. We also show that in short intervals of certain lengths the divisor function has a Gaussian limiting distribution. The analogous problems for Hecke eigenvalues are also considered.

5 citations

Journal ArticleDOI
TL;DR: In this article, it was shown that the affine plane is characterized by the weighted dual graph of the boundary divisor of the minimal normal compactification of Ω{A}^{2}.
Abstract: Morrow [9] classified all weighted dual graphs of the boundary of the minimal normal compactifications of the affine plane $\mathbf{A}^{2}$ by using a result of Ramanujam [10] that any minimal normal compactification of $\mathbf{A}^{2}$ has a linear chain as the graph of the boundary divisor. In this article, we give a new proof of the above-mentioned results of Ramanujam-Morrow [9] from a different point of view and by the purely algebro-geometric arguments. Moreover, we show that the affine plane $\mathbf{A}^{2}$ is characterized by the weighted dual graph of the boundary divisor.

5 citations

Posted Content
TL;DR: In this article, the authors used filtered log-$\mathscr{D}$-modules to represent the (dual) localization of Saito's Mixed Hodge Modules along a smooth hypersurface.
Abstract: We use filtered log-$\mathscr{D}$-modules to represent the (dual) localization of Saito's Mixed Hodge Modules along a smooth hypersurface, and show that they also behave well under the direct image functor and the dual functor in the derived category of filtered log-$\mathscr{D}$-modules. The results of this paper can be used to generalize the result of M. Popa and C. Schnell about Kodaira dimension and zeros of holomorphic one-forms into the log setting.

5 citations

Proceedings ArticleDOI
01 Jan 2020
TL;DR: In this paper, the Pontryagin dual of the adjoint Selmer group of an induced representation of a real quadratic field was shown to be canonically isomorphic to a local ring of a Hecke algebra.
Abstract: We study the universal minimal ordinary Galois deformation $\rho_{\mathbb{T}}$ of an induced representation $\operatorname{Ind}_F^{\mathbb{Q}} \varphi$ from a real quadratic field $F$ with values in $\mathrm{GL}_2(\mathbb{T})$. By Taylor–Wiles, the universal ring $\mathbb{T}$ is isomorphic to a local ring of a Hecke algebra. Combining an idea of Cho–Vatsal [CV03] with a modified Taylor–Wiles patching argument in [H17], under mild assumptions, we show that the Pontryagin dual of the adjoint Selmer group of $\rho_{\mathbb{T}}$ is canonically isomorphic to $\mathbb{T}/(L)$ for a non-zero divisor $L \in \mathbb{T}$ which is a generator of the different $\mathfrak{d}_{\mathbb{T}/\Lambda}$ of $\mathbb{T}$ over the weight Iwasawa algebra $\Lambda=W[[T]]$ inside $\mathbb{T}$. Moreover, defining $\langle\varepsilon\rangle := (1+T)^{\log_p(\varepsilon)/\log_p(1 + p)}$ for a fundamental unit $\varepsilon$ of the real quadratic field $F$, we show that the adjoint Selmer group of $\operatorname{Ind}_F^\mathbb{Q}\Phi$ for the (minimal) universal character $\Phi$ deforming $\varphi$ is isomorphic to $\Lambda/(\langle\varepsilon\rangle - 1)$ as $\Lambda$-modules.

5 citations

Patent
Mitsuyoshi Yao1, Kohichi Ueda1
17 Mar 1994
TL;DR: In this article, a divider circuit which calculates an integral quotient of an integral divisor and an integral dividend is considered, where an activation unit sets a new operational integer by canceling the subordinate n bits of the difference and causes the calculation unit to set the integral dividend, specify a product and calculate a difference based on the new operational integers.
Abstract: A divider circuit which calculates an integral quotient of an integral divisor and an integral dividend. A first multiplication unit calculates products of the integral divisor and all n-bit pattern values of an n-bit pattern, where n is a predetermined number and the n-bit pattern values respectively correspond to the calculated products. A calculation unit sets the integral dividend as an initial value of an operational integer, specifies a product among the products calculated by the first multiplication unit of which the subordinate n-bit value is equal to the subordinate n-bit value of the operational integer, and calculates a difference of the operational integer and the specified product. When the difference calculated by the calculation unit is not zero, an activation unit sets a new operational integer by canceling the subordinate n bits of the difference and causes the calculation unit to set the integral dividend, specify a product and calculate a difference based on the new operational integer. An output unit successively takes n-bit pattern values respectively corresponding to products specified by the calculation unit, and outputs these n-bit pattern values as the quotient when the difference calculated by the calculation unit is zero.

4 citations


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