TY - JOUR
T1 - On a variant of the Ailon–Rudnick theorem in finite characteristic
AU - Ghioca, Dragos
AU - Hsia, Liang Chung
AU - Tucker, Thomas J.
N1 - Funding Information:
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.
Publisher Copyright:
© 2017, University at Albany. All rights reserved.
PY - 2017/2/20
Y1 - 2017/2/20
N2 - Let L be a field of characteristic p, and let a, b, c, d ε 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 ε L satisfying f(a(λ)) = c(λ) and g(b(λ)) = d(λ) for some polynomials f, g ε 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.
AB - Let L be a field of characteristic p, and let a, b, c, d ε 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 ε L satisfying f(a(λ)) = c(λ) and g(b(λ)) = d(λ) for some polynomials f, g ε 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.
KW - Ailon-Rudnick theorem
KW - Weil height
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M3 - Article
AN - SCOPUS:85013821286
SN - 1076-9803
VL - 23
SP - 213
EP - 225
JO - New York Journal of Mathematics
JF - New York Journal of Mathematics
ER -