Arithmetical properties of a certain power series

Kumiko Nishioka, Iekata Shiokawa, Jun Ichi Tamura

研究成果: Article査読

17 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)61-87
ページ数27
ジャーナルJournal of Number Theory
42
1
DOI
出版ステータスPublished - 1992 9月

ASJC Scopus subject areas

  • 代数と数論

フィンガープリント

「Arithmetical properties of a certain power series」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル