Guoyou Qian

activity

20092019

most citedUniform lower bound for the least common multiple of a polynomial sequence

1 citations · 1 across the 5 of their papers we have counts for

collaborators

9 papers

math.NT2019

The distribution of divisors of polynomials

Kevin Ford, Guoyou Qian

Let $F (x)$ be an irreducible polynomial with integer coefficients and degree at least 2. For $x \geq z \geq y \geq 2$ , denote by $H_{F} (x, y, z)$ the number of integers $n \leq x$ such that…

math.NT2014

Asymptotic behavior of the least common multiple of consecutive reducible quadratic progression terms

Guoyou Qian, Shaofang Hong

Let $l$ and $m$ be two integers with $l > m \geq 0$ , and let $f (x)$ be the product of two linear polynomials with integer coefficients. In this paper, we show that $\log {\rm lcm}_{mn<…

math.NT2014

New results on permutation polynomials over finite fields

Xiaoer Qin, Guoyou Qian, Shaofang Hong

In this paper, we get several new results on permutation polynomials over finite fields. First, by using the linear translator, we construct permutation polynomials of the forms $L…

math.NT2014

The elementary symmetric functions of a reciprocal polynomial sequence

Yuanyuan Luo, Shaofang Hong, Guoyou Qian +1

Erdös and Niven proved in 1946 that for any positive integers $m$ and $d$ , there are at most finitely many integers $n$ for which at least one of the elementary symmetric functions…

math.NT2013★ 1 cited

Uniform lower bound for the least common multiple of a polynomial sequence

Shaofang Hong, Yuanyuan Luo, Guoyou Qian +1

Let $n$ be a positive integer and $f (x)$ be a polynomial with nonnegative integer coefficients. We prove that $lcm_{⌈ n /2 ⌉ \leq i \leq n} {f (i)} \geq 2^{n}$ except that…

math.NT2012

The least common multiple of consecutive quadratic progression terms

Shaofang Hong, Guoyou Qian

Let $k$ be an arbitrary given positive integer and let $f (x) \in Z [x]$ be a quadratic polynomial with $a$ and $D$ as its leading coefficient and discriminant, respectively…