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, the authors established an asymptotic formula for the sum of the sum √ √ x < n \leqq x + y √ 1/2 log x when y is large compared to x.
Abstract: In this paper we establish an asymptotic formula for the sum
$$ {\sum\limits_{x < n \leqq x + y} {d_{4} (n)} } $$
when y is large compared to x
1/2 log x.
7 citations
TL;DR: In this paper, it was shown that the Kodaira embedding induced by orthonormal basis of the Bergman space of kA is K-semistable on a smooth projective manifold.
Abstract: Let $$\hat{L}$$
be the projective completion of an ample line bundle L over D, a smooth projective manifold. Hwang-Singer et al. (Trans Am Math Soc 354(6):2285–2325, 1998) have constructed complete CSCK metric on $$\hat{L}{\backslash }D$$
. When the corresponding Kahler form is in the cohomology class of a rational divisor A and when L has negative CSCK metric on D, we show that the Kodaira embedding induced by orthonormal basis of the Bergman space of kA is almost balanced. As a corollary, $$(\hat{L},D,cA,0)$$
is K-semistable.
7 citations
TL;DR: In this article, it was shown that if b > 1 is a fixed positive integer, then the Euler function of n has only finitely many positive integer solutions (x, y, m, n).
Abstract: For a positive integer n we write φ(n) for the Euler function of n. In this note, we show that if b > 1 is a fixed positive integer, then the equation
$$ \varphi \left( {x\frac{{b^n - 1}} {{b - 1}}} \right) = y\frac{{b^m - 1}} {{b - 1}}, where x,y \in \{ 1, \ldots ,b - 1\} , $$
has only finitely many positive integer solutions (x, y, m, n).
7 citations
TL;DR: In this article, all possible weight enumerators for every irreducible cyclic code of length n over a finite field were shown explicitly, in the case that each prime divisor of n is also a divisors of n.
Abstract: In this article, we show explicitly all possible weight enumerators for every irreducible cyclic code of length $$n$$n over a finite field $${\mathbb {F}}_q$$Fq, in the case which each prime divisor of $$n$$n is also a divisor of $$q-1$$q-1.
7 citations
TL;DR: For integers a, b not both zero, let the symbol (a, b)** denote the greatest unitary divisor of both a and b as discussed by the authors, where b is the smallest positive integer.
Abstract: It is well-known that a divisor d > 0 of the positive integer n is called unitary, if dδ = n and (d, δ) = 1. For integers a, b not both zero, let the symbol (a, b)** denote the greatest unitary divisor of both a and b. A divisor d>0 of the positive integer n is called bi-unitary, if dδ = n and (d, δ)** = 1.
7 citations