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Dragos Ghioca, Liang-Chung Hsia, and Thomas J. Tucker
On a variant of the Ailon-Rudnick theorem in finite characteristic view print
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| Published: |
February 20, 2017
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| Keywords: |
Ailon-Rudnick theorem, Weil height |
| Subject: |
Primary 11G50; Secondary 11G35, 14G25 |
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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.
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| 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.
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| 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
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