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 article, the existence of incomplete Kahler-Einstein metrics on quasi-projective varieties with cone-edge type singularities along a divisor was studied, and it was shown that if these metrics exist for all small cone-angles, then they exist in a uniform interval of angles depending on the dimension.
Abstract: Tian initiated the study of incomplete Kahler-Einstein metrics on quasi-projective varieties with cone-edge type singularities along a divisor, described by the cone-angle $2\pi(1-\alpha)$ for $\alpha\in (0, 1)$. In this paper we study how the existence of such Kahler-Einstein metrics depends on $\alpha$. We show that in the negative scalar curvature case, if such Kahler-Einstein metrics exist for all small cone-angles then they exist for every $\alpha\in(\frac{n+1}{n+2}, 1)$, where $n$ is the dimension. We also give a characterization of the pairs that admit negatively curved cone-edge Kahler-Einstein metrics with cone angle close to $2\pi$. Again if these metrics exist for all cone-angles close to $2\pi$, then they exist in a uniform interval of angles depending on the dimension only. Finally, we show how in the positive scalar curvature case the existence of such uniform bounds is obstructed.
8 citations
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TL;DR: In this paper, the authors studied the family of algebraic K3 surfaces generated by the smooth intersection of a (1, 1) form and a (2, 2) form in the Picard number 3.
Abstract: In this paper, we study the family of algebraic K3 surfaces generated by the smooth intersection of a (1, 1) form and a (2, 2) form in \(\mathbb{P}^{2} { \times }\mathbb{P}^{2} \) defined over \(\mathbb{C}\) and with Picard number 3. We describe the group of automorphisms \(\mathcal{A} = Aut (V / {\mathbb{C}})\) on V. For an ample divisor D and an arbitrary curve C0 on V, we investigate the asymptotic behavior of the quantity \(N_{\mathcal{A}{\text{(}}C_0 {\text{)}}} (t) = \# \{ C \in \mathcal{A}{\text{(}}C_0 {\text{)}}\;{\text{:}}\;C \cdot D < t\} \). We show that the limit
$$\mathop {\lim }\limits_{t \to \infty } \frac{{\log N_{\mathcal{A}(C)} (t)}}{{\log t}} = \alpha $$
exists, does not depend on the choice of curve C or ample divisor D, and that .6515<α<.6538.
8 citations
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01 Dec 2010TL;DR: In this paper, a phase error compensation block is used to compensate for the effects of using the other-than-two divisor in a multi-band multi-channel receiver.
Abstract: Some embodiments of the present disclosure relate to multiband receivers that include at least one divider unit having a divisor that is other-than-two For example, in some embodiments the divisor is an odd integer (eg, three) Such divisors allow oscillators for respective receiver subunits in a multi-band receiver to have frequencies that are sufficiently different from one another so as to limit cross-talk interference there between, even when the receiver subunits are concurrently receiving data on adjacent channels To facilitate this other-than-two divisor, a phase error compensation block is often used to compensate for the effects of using the other-than-two divisor
8 citations
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TL;DR: In this paper, it was shown that if E has CM, then for all but o(x/ log x) of primes p ≤ x, the set of functions of p such that ∊(p) → 0 as p → ∞ has density zero.
Abstract: Let E be an elliptic curve defined over ℚ. Let Γ be a free subgroup of rank r of E(ℚ). For any prime p of good reduction, let Γp be the reduction of Γ modulo p and Ep be the reduction of E modulo p. We prove that if E has CM then for all but o(x/ log x) of primes p ≤ x, \[ |\Gamma_p| \geq p^{\frac{r}{r+2}+\epsilon(p)}, \] where ∊(p) is any function of p such that ∊(p) → 0 as p → ∞. This is a consequence of two other results. Denote by Np the cardinality of Ep(𝔽p), where 𝔽p is a finite field of p elements. Then for any δ > 0, the set of primes p for which Np has a divisor in the range (pδ - ∊(p), pδ + ∊(p)) has density zero. Moreover, the set of primes p for which $|\Gamma_p| < p^{\frac{r}{r+2} - \epsilon(p)}$ has density zero.
8 citations
01 Jan 2007
TL;DR: In this paper, the authors studied the problem of counting the number of positive integers n! x which have a divisor d > z with the property that p! y for every prime p dividing d.
Abstract: We study the function ! (x,y,z) that counts the number of positive integers n ! x which have a divisor d > z with the property that p ! y for every prime p dividing d. We also indicate some cryptographic applications of our results.
8 citations