Unlikely intersection for two-parameter families of polynomials

Dragos Ghioca, Liang Chung Hsia, Thomas J. Tucker

Research output: Contribution to journalArticle

1 Citation (Scopus)

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 languageEnglish
Pages (from-to)7589-7618
Number of pages30
JournalInternational Mathematics Research Notices
Volume2016
Issue number24
DOIs
Publication statusPublished - 2016 Jan 1

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Affine plane
Complex number
Two Parameters
Intersection
Distinct
Polynomial
Integer
Family

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 journalArticle

Ghioca, Dragos ; Hsia, Liang Chung ; Tucker, Thomas J. / Unlikely intersection for two-parameter families of polynomials. In: International Mathematics Research Notices. 2016 ; Vol. 2016, No. 24. pp. 7589-7618.
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