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

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

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

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 F p . 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 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.

Original languageEnglish
Pages (from-to)213-225
Number of pages13
JournalNew York Journal of Mathematics
Volume23
Publication statusPublished - 2017 Feb 20

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Keywords

  • Ailon-Rudnick theorem
  • Weil height

ASJC Scopus subject areas

  • Mathematics(all)

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