Unlikely intersection for two-parameter families of polynomials

Dragos Ghioca; Liang Chung Hsia; Thomas J. Tucker

doi:10.1093/imrn/rnw006

Unlikely intersection for two-parameter families of polynomials

Dragos Ghioca^*
, Liang Chung Hsia
, Thomas J. Tucker

^*此作品的通信作者

數學系

研究成果: 雜誌貢獻 › 期刊論文 › 同行評審

4 引文斯高帕斯（Scopus）

摘要

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 c_i is preperiodic for the action of the polynomial x^d + ax + b is not Zariski dense in the affine plane.

原文	英語
頁（從 - 到）	7589-7618
頁數	30
期刊	International Mathematics Research Notices
卷	2016
發行號	24
DOIs	https://doi.org/10.1093/imrn/rnw006
出版狀態	已發佈 - 2016 12月

ASJC Scopus subject areas

一般數學

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10.1093/imrn/rnw006

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引用此

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title = "Unlikely intersection for two-parameter families of polynomials",

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.",

author = "Dragos Ghioca and Hsia, \{Liang Chung\} and Tucker, \{Thomas J.\}",

year = "2016",

month = dec,

doi = "10.1093/imrn/rnw006",

language = "English",

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TY - JOUR

T1 - Unlikely intersection for two-parameter families of polynomials

AU - Ghioca, Dragos

AU - Hsia, Liang Chung

AU - Tucker, Thomas J.

PY - 2016/12

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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.

UR - https://www.scopus.com/pages/publications/85014403738

UR - https://www.scopus.com/pages/publications/85014403738#tab=citedBy

U2 - 10.1093/imrn/rnw006

DO - 10.1093/imrn/rnw006

M3 - Article

AN - SCOPUS:85014403738

SN - 1073-7928

VL - 2016

SP - 7589

EP - 7618

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

IS - 24

ER -

Unlikely intersection for two-parameter families of polynomials

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