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.

The average value of divisor sums in arithmetic progressions

Abstract: Let α(n) denote the Fourier coefficients of cusp forms or the number of divisors of n. Estimates of the typeare shown, uniformly in q ≤ X. The methods can be extended to other arithmetic functions, for example, the number of representations of n as a sum of two squares or k-free numbers. As an application, sums of the type ∑ n ≤ X α(n) ψ(n) for any q-periodic function ψ can be estimated non-trivially.

Fast Genus Three Hyperelliptic Curve Cryptosystems

Abstract: This paper presents a fast addition algorithm for the divisor class groups of genus three hyperelliptic curves. This algorithm improves the most recently proposed Harley algorithm for genus three hyperelliptic curves, which have brought up a noticeable progress since the well known Cantor algorithm. In this paper, we extend the Harley algorithm to genus three curves. The computational cost of the proposed algorithm is I +8 1M for an addition and I +7 4M for a doubling. (Here I and M denote the cost of an inversion and a multiplication on the definition fields.) We also show the implementation of the algorithm on Alpha 21264 / 667MHz, which takes 932 µs for a 160bit scalar multiplication on a divisor class group.

A Note on an Estimator for the Variance That Utilizes the Kurtosis

Abstract: An estimator (S W 2) for the variance is developed by minimizing the mean squared error (MSE) using a generalized weight for the sum of squares instead of 1/(n − 1). The optimal divisor found is (n + 1) + (α4 − 3) (n 1 1)/n, where α4 is the kurtosis. For the normal distribution (α4 = 3), the divisor becomes n + 1. Generally, for kurtosis greater than 3 the divisor will be greater than n + 1 and for kurtosis less than 3 the divisor will be less than n + 1. Using n + 1 as a divisor will result in a smaller MSE for distributions with α4 > 3.

The Erdős–Ko–Rado Theorem for Integer Sequences

Abstract: , q, t we determine the maximum number of integer sequences \(\) which satisfy \(\) for \(\), and any two sequences agree in at least t positions. The result gives an affirmative answer to a conjecture of Frankl and Furedi.

Asymptotically cylindrical Calabi-Yau manifolds

Abstract: Let $M$ be a complete Ricci-flat Kahler manifold with one end and assume that this end converges at an exponential rate to $[0,\infty) \times X$ for some compact connected Ricci-flat manifold $X$. We begin by proving general structure theorems for $M$; in particular we show that there is no loss of generality in assuming that $M$ is simply-connected and irreducible with $\mathrm{Hol}(M) = \mathrm{SU}(n)$, where $n$ is the complex dimension of $M$. If $n \gt 2$ we then show that there exists a projective orbifold $\overline{M}$ and a divisor $\overline{D} \in \lvert -K_{\overline{M}} \rvert$ with torsion normal bundle such that $\overline{M}$ is biholomorphic to $\overline{M} \setminus \overline{D}$, thereby settling a long-standing question of Yau in the asymptotically cylindrical setting.We give examples where $\overline{M}$ is not smooth: the existence of such examples appears not to have been noticed previously. Conversely, for any such pair $\overline{M} \setminus \overline{D}$ we give a short and self-contained proof of the existence and uniqueness of exponentially asymptotically cylindrical Calabi–Yau metrics on $\overline{M} \setminus \overline{D}$.