### 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 |

### Fingerprint

### Keywords

- Ailon-Rudnick theorem
- Weil height

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*New York Journal of Mathematics*,

*23*, 213-225.

**On a variant of the Ailon–Rudnick theorem in finite characteristic.** / Ghioca, Dragos; Hsia, Liang-Chung; Tucker, Thomas J.

Research output: Contribution to journal › Article

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

}

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.

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 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.

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 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.

KW - Ailon-Rudnick theorem

KW - Weil height

UR - http://www.scopus.com/inward/record.url?scp=85013821286&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85013821286&partnerID=8YFLogxK

M3 - Article

VL - 23

SP - 213

EP - 225

JO - New York Journal of Mathematics

JF - New York Journal of Mathematics

SN - 1076-9803

ER -