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 for a torsion point of prime order, there always exists a primitive divisor, and the link between the study of the primitive disambiguation and the Lang-Trotter conjecture was established.
Abstract: Let $\{nP+Q\}_{n\geq0}$ be a sequence of points on an elliptic curve defined over a number field $K$. In this paper, we study the denominators of the $x$-coordinates of this sequence. We prove that, if $Q$ is a torsion point of prime order, then for $n$ large enough there always exists a primitive divisor. Later on, we show the link between the study of the primitive divisors and the Lang-Trotter conjecture.
1 citations
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TL;DR: In this article, a weighted divisor function with congruence conditions was studied and the upper bound, mean value, mean square, and power-moments were established.
Abstract: We study a weighted divisor function $\mathop{{\sum}'}\limits_{mn\leq x}\cos(2\pi m\theta_1)\sin(2\pi n\theta_2)$, where $\theta_i (0<\theta_i<1)$ is a rational number. By connecting it with the divisor problem with congruence conditions, we establish the upper bound, mean-value, mean-square and some power-moments.
1 citations
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TL;DR: X is an algebraic submanifold of the complex projective space P of dimension 5 whose intersection with some hyperplane is a smooth simply normal crossing divisor such that g(A_{k), L_{A_k}) \leq 1 for k=1,\ldots, r.
Abstract: Let X be an algebraic submanifold of the complex projective space
$\mathbb{P}^N$ of dimension $n \geq 5$. We describe those
$X \subset \mathbb{P}^N$ whose intersection with some hyperplane is a smooth simply
normal crossing divisor $A_{1} + \cdots + A_{r}$ with $r \geq 2$ such that
$g(A_{k}, L_{A_k}) \leq 1$ for $k=1,\ldots, r$.
1 citations
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TL;DR: In this paper, the average orders of a class of divisor functions defined by symmetric polynomials on the multi-set of prime factors of a number were studied.
Abstract: We compute the average orders and study the distribution of values of a class of divisor functions defined by symmetric polynomials on the multi-set of prime factors of a number. These generalize those we have previously defined. The simplest case of these functions is the sum of prime factors with repetition function, whose average order has been computed in various ways by Alladi and Erd˝os, LeVan,and Kerawala.
1 citations