
A note on intersective polynomials in function fields
 QIAN Kun, LIU Baoqing, LI Guoquan

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(12):
8696.
doi:10.6040/j.issn.16719352.0.2018.710

Abstract
(
234 )
PDF (439KB)
(
101
)
Save

References 
Related Articles 
Metrics
Let Z denote the ring of rational integers. Let L be a field, and let p be its characteristic. Let f(x)=∑^{n}_{j=0}a_{j}x^{j}∈L［x］, the polynomial ring over L. Suppose that f(x)=a∏^{r}_{i=1}(xη_{i})^{ei} over some algebraic closure of L, where a∈L, all the η_{i} are distinct, and r,e_{}1,e_{}2,…,e_{r} are positive integers with r≥2 and n=∑^{r}_{j=}1e_{j}. The semidiscriminant Δ(f) of f is defined by Δ(f)=a^{}2n1∏_{}1≤i,j≤r_{i≠j}(η_{i}η_{j})^{ei ej}. It is proved that if n<p, then there exist a positive integer m with mn! and a polynomial G∈Z［x_{0},x_{1},…,x_{n}］, which depend only on the vector (e_{}1,e_{}2,…,e_{r}), such that Δ(f)=1/mG(a_{}0,a_{}1,…,a_{n}). This result is applied to investigate a question on intersective polynomials over the ring L［x］, where L is a finite field.