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

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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 c_i is preperiodic for the action of the polynomial x^d + 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	https://doi.org/10.1093/imrn/rnw006
Publication status	Published - 2016

ASJC Scopus subject areas

Mathematics(all)

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10.1093/imrn/rnw006

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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.}",

note = "Funding Information: This work was partially supported by NSERC [to D.G.]; NSF Grants DMS-0854839 and DMS-1200749 [to T.J.T.], and NSC Grant 102-2115-M-003-002-MY2 [to L.-C.H.] and supported by NCTS [to L.-C.H.].",

year = "2016",

doi = "10.1093/imrn/rnw006",

language = "English",

volume = "2016",

pages = "7589--7618",

journal = "International Mathematics Research Notices",

issn = "1073-7928",

publisher = "Oxford University Press",

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T1 - Unlikely intersection for two-parameter families of polynomials

AU - Ghioca, Dragos

AU - Hsia, Liang Chung

AU - Tucker, Thomas J.

N1 - Funding Information: This work was partially supported by NSERC [to D.G.]; NSF Grants DMS-0854839 and DMS-1200749 [to T.J.T.], and NSC Grant 102-2115-M-003-002-MY2 [to L.-C.H.] and supported by NCTS [to L.-C.H.].

PY - 2016

Y1 - 2016

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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JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

SN - 1073-7928

IS - 24

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