### 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 language | English |
---|---|

Pages (from-to) | 213-225 |

Number of pages | 13 |

Journal | New York Journal of Mathematics |

Volume | 23 |

Publication status | Published - 2017 Feb 20 |

### Keywords

- Ailon-Rudnick theorem
- Weil height

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Ghioca, D., Hsia, L-C., & Tucker, T. J. (2017). On a variant of the Ailon–Rudnick theorem in finite characteristic.

*New York Journal of Mathematics*,*23*, 213-225.