New York Journal of Mathematics
Volume 23 (2017) 213-225


Dragos Ghioca, Liang-Chung Hsia, and Thomas J. Tucker

On a variant of the Ailon-Rudnick theorem in finite characteristic

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Published: February 20, 2017
Keywords: Ailon-Rudnick theorem, Weil height
Subject: Primary 11G50; Secondary 11G35, 14G25

Let L be a field of characteristic p, and let a,b,c,d∈ L(T). Assume that a and b are algebraically independent over Fp. Then for each fixed positive integer n, we prove that there exist at most finitely many λ∈ \Lbar satisfying f(a(λ)) = c(λ) and g(b(λ))=d(λ) for some polynomials f,g∈ Fpn[Z] such that f(a)≠ c and g(b)≠ d. Our result is a characteristic p variant of a related statement proven by Ailon and Rudnick.


The research of the first author was partially supported by an NSERC Discovery grant. The second author was supported by MOST grant 104-2115-M-003-004-MY2. The third author was partially supported by NSF Grant DMS-1501515.

Author information

Dragos Ghioca:
Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada

Liang-Chung Hsia:
Department of Mathematics, National Taiwan Normal University, Taipei, Taiwan, ROC

Thomas J. Tucker:
Department of Mathematics, University of Rochester, Rochester, NY 14627, USA