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

view    print


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

Abstract
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.

Acknowledgements

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
dghioca@math.ubc.ca

Liang-Chung Hsia:
Department of Mathematics, National Taiwan Normal University, Taipei, Taiwan, ROC
hsia@math.ntnu.edu.tw

Thomas J. Tucker:
Department of Mathematics, University of Rochester, Rochester, NY 14627, USA
ttucker@math.rochester.edu