## Abstract

Let f(x) be a power series ∑_{n≥1} ζ(n)x^{e(n)}, where (e(n)) is a strictly increasing linear recurrence sequence of nonnegative integers, and (ζ(n)) a sequence of roots of unity in ℚ_{p} satisfying an appropriate technical condition. Then we are mainly interested in characterizing the algebraic independence over ℚ_{p} of the elements f(α_{1}),…, f(α_{t}) from ℂ_{p} in terms of the distinct α_{1},…, α_{t} ∈ ℚ_{p} satisfying 0 < |α_{τ} |p < 1 for τ = 1,…, t. A striking application of our basic result says that, in the case e(n) = n, the set {f(α)| α ∈ ℚ_{p}, 0 < |α|_{p} < 1} is algebraically independent over ℚ_{p} if (ζ(n)) satisfies the “technical condition”. We close with a conjecture concerning more general sequences (e(n)).

Original language | English |
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Pages (from-to) | 519-533 |

Number of pages | 15 |

Journal | Journal de Theorie des Nombres de Bordeaux |

Volume | 16 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2004 |

## ASJC Scopus subject areas

- Algebra and Number Theory

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