 

Dragos Ghioca, LiangChung Hsia, and Thomas J. Tucker
On a variant of the AilonRudnick theorem in finite characteristic view print


Published: 
February 20, 2017

Keywords: 
AilonRudnick 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∈ F_{pn}[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 1042115M003004MY2. The third author was partially supported by NSF Grant DMS1501515.


Author information
Dragos Ghioca:
Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada
dghioca@math.ubc.ca
LiangChung 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

