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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TL;DR: In this paper, it was shown that a surface containing an exceptional divisor with arithmetic genus at least two is slope unstable for some polarisation, and for surfaces with non-negative Kodaira dimension any destabilising divisors must have negative self-intersection and arithmetic genus with at least 2.
Abstract: We study slope stability of smooth surfaces and its connection with exceptional divisors. We show that a surface containing an exceptional divisor with arithmetic genus at least two is slope unstable for some polarisation. In the converse direction we show that slope stability of surfaces can be tested with divisors, and prove that for surfaces with non-negative Kodaira dimension any destabilising divisor must have negative self-intersection and arithmetic genus at least two. We also prove that a destabilising divisor can never be nef, and as an application give an example of a surface that is slope stable but not K-stable.
2 citations
TL;DR: In this paper, the authors give an explicit basis for the group of modular units on $X(Gamma)$ that have divisors defined over $\mathbb{Q}$.
Abstract: For $p\!>\!3$ an odd prime, let $\Gamma$ be a congruence subgroup between $\Gamma_1(p)$ and $\Gamma_0(p)$. In this article, we give an explicit basis for the group of modular units on $X(\Gamma)$ that have divisors defined over $\mathbb{Q}$. As an application, we determine the order of the cuspidal $\mathbb{Q}$-rational torsion subgroup of $J(\Gamma)$ generated by the divisor classes of cuspidal divisors of degree $0$ defined over $\mathbb Q$.
2 citations
Patent•
04 Oct 2006
TL;DR: In this paper, an equivalence which gives the same remainder value as a divisor n is computed as a value relating to a Montgomery conversion parameter used in a Montgomery multiplication remainder operation.
Abstract: A computation method for use in cryptography which employs the Montgomery modular multiplication algorithm. To speed up the computation process, an equivalence which gives the same remainder value as a divisor n is computed as a value relating to a Montgomery conversion parameter used in a Montgomery multiplication remainder operation. That is, the method calculates an equivalence H 0 = 2 m*k+1 (mod n) relating to a divisor n of 2 m*k+1 (step A), computes an equivalence H = 2 E(p, m, k) (mod n) of 2 E(p, m, k) (mod n) from H 0 by an REDC operation (step B), and performs a correction operation by H = REDC (H, G) n for g = 2 k*G/p, m, k ) when 2 P > mxk (step C).
2 citations
TL;DR: New proofs for the classical bounds P(x) « x 1/3, Δ(x), h 1/ 3 log x are given in this article, where P denotes the error term in the classical circle, and Δ (x) denotes the classical divisor problem.
Abstract: New proofs for the classical bounds P(x) « x1/3, Δ(x) « h1/3 log x are given. Here P(x) denotes the error term in the classical circle, and Δ (x) in the classical divisor problem. .
2 citations
TL;DR: In this paper, the Smith normal form and the transforming matrices of the left greatest common divisor of matrices have been studied, one of which is a disappear matrix.
Abstract: We study the structure of the greatest common divisor of matrices one of which is a disappear matrix. In this connection, we indicate the Smith normal form and the transforming matrices of the left greatest common divisor.
2 citations