Arithmetical properties of a certain power series

Kumiko Nishioka, Iekata Shiokawa, Jun Ichi Tamura

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Abstract

The function f(θ, φ; x, y) = Σk = 1 Σ1 ≤ m ≤ kθ + φ xkym, where θ > 0 is irrational and φ is real, satisfies Mahler-type functional equations which enable us to represent it by a gap-like series and then by a continued fraction. Using these representations, we describe the sequence {[(k + 1) θ + φ] - [kθ + φ]}k = 1 by a chain of substitutions and give algebraic independence results for the values of f(θ, φ, x, y) at some algebraic points when the partial quotients of the continued fraction of θ are unbounded, and irrationality measures for the values at some rational points.

Original languageEnglish
Pages (from-to)61-87
Number of pages27
JournalJournal of Number Theory
Volume42
Issue number1
DOIs
Publication statusPublished - 1992 Sep

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ASJC Scopus subject areas

  • Algebra and Number Theory

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