RATIONAL APPROXIMATIONS OF (1 + x)a AND APPLICATIONS TO THUE INEQUALITIES

• TANAKA Yuzen

  c/o Hironori Shiga Graduate School of Science and Technology Institute of Mathematics and Physics Chiba University

抄録

We study some Padé approximations to (1 + x)^a and we give their lower bound using Rickert's theorem, where a and x are rational numbers in the open interval (0, 1) with (denominator of x) > (numerator of x)²×(denominator of a)^3/2. Thenwe give an effective bound for the solutions of the Thue inequalities |Xⁿ-(1+x)^αY ⁿ| ≤ k for a positive integer n and rational numbers α, x with n ≥ 2 and 0 < α/n, x < 1 and a positive real number k. As an application we solve these inequalities for some special cases. Our result depends on the methods of Chudnovsky [C], Rickert [R] and Wakabayashi [W1, W2].

収録刊行物

• 九州数学雑誌

  九州数学雑誌 57 (2), 277-290, 2003

  九州大学大学院数理学研究院

キーワード

• General Mathematics

詳細情報

• CRID: 1390282680206566400
• NII論文ID: 80017501683
• NII書誌ID: AA10994346
• DOI: 10.2206/kyushujm.57.277
• ISSN: 18832032
• ISSN: 13406116
• MRID: 2050086
• Web Site: https://www.jstage.jst.go.jp/article/kyushujm/57/2/57_2_277/_pdf
• 本文言語コード: en
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