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

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 Jan 1

ASJC Scopus subject areas

Mathematics(all)

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10.1093/imrn/rnw006

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Ghioca, D., Hsia, L. C., & Tucker, T. J. (2016). Unlikely intersection for two-parameter families of polynomials. International Mathematics Research Notices, 2016(24), 7589-7618. https://doi.org/10.1093/imrn/rnw006

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