Remarkable algebraic independence property of certain series related to continued fractions

研究成果: Conference contribution

抄録

We prove, using Mahler's method, the following results: Theorem 1 asserts that the series Θx,a,q) are algebraically independent for any distinct triplets (x,a,q) of nonzero algebraic numbers, where Θ (x,a,q) has the property shown in Corollary 1 that Θ (a,a,q) is expressed as a continued fraction. Theorem 2 asserts, under the weaker condition than that of Theorem 1, that the values Θ(x,1,q) are algebraically independent for any distinct pairs (x,q) of nonzero algebraic numbers. Typical examples of these results are generated by Fibonacci numbers.

本文言語English
ホスト出版物のタイトルDiophantine Analysis and Related Fields, DARF 2007/2008
ページ190-204
ページ数15
DOI
出版ステータスPublished - 2008 12 1
イベントDiophantine Analysis and Related Fields, DARF 2007/2008 - Kyoto, Japan
継続期間: 2008 3 52008 3 7

出版物シリーズ

名前AIP Conference Proceedings
976
ISSN(印刷版)0094-243X
ISSN(電子版)1551-7616

Other

OtherDiophantine Analysis and Related Fields, DARF 2007/2008
国/地域Japan
CityKyoto
Period08/3/508/3/7

ASJC Scopus subject areas

  • 物理学および天文学(全般)

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