Abstract
Let c1, c2, c3 be distinct complex numbers, and let d ≥ 3 be an integer. We show that the set of all pairs (a, b) ϵ C × C such that each ci is preperiodic for the action of the polynomial xd + ax + b is not Zariski dense in the affine plane.
| Original language | English |
|---|---|
| Pages (from-to) | 7589-7618 |
| Number of pages | 30 |
| Journal | International Mathematics Research Notices |
| Volume | 2016 |
| Issue number | 24 |
| DOIs | |
| Publication status | Published - 2016 Jan 1 |
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ASJC Scopus subject areas
- Mathematics(all)
Cite this
Unlikely intersection for two-parameter families of polynomials. / Ghioca, Dragos; Hsia, Liang-Chung; Tucker, Thomas J.
In: International Mathematics Research Notices, Vol. 2016, No. 24, 01.01.2016, p. 7589-7618.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Unlikely intersection for two-parameter families of polynomials
AU - Ghioca, Dragos
AU - Hsia, Liang-Chung
AU - Tucker, Thomas J.
PY - 2016/1/1
Y1 - 2016/1/1
N2 - Let c1, c2, c3 be distinct complex numbers, and let d ≥ 3 be an integer. We show that the set of all pairs (a, b) ϵ C × C such that each ci is preperiodic for the action of the polynomial xd + ax + b is not Zariski dense in the affine plane.
AB - Let c1, c2, c3 be distinct complex numbers, and let d ≥ 3 be an integer. We show that the set of all pairs (a, b) ϵ C × C such that each ci is preperiodic for the action of the polynomial xd + ax + b is not Zariski dense in the affine plane.
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UR - http://www.scopus.com/inward/citedby.url?scp=85014403738&partnerID=8YFLogxK
U2 - 10.1093/imrn/rnw006
DO - 10.1093/imrn/rnw006
M3 - Article
VL - 2016
SP - 7589
EP - 7618
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
SN - 1073-7928
IS - 24
ER -