### 抄録

In this paper we establish, using Mahler’s method, the algebraic independence of the values at an algebraic number of power series closely related to decimal expansion of linearly independent positive numbers. First we consider a simpler case in Theorem 1 and then generalize it to Theorem 3, which includes Nishioka’s result quoted as Theorem 2 of this paper. Lemma 7 plays an essential role in the proof of Theorems 1 and 3.

元の言語 | English |
---|---|

ページ（範囲） | 367-380 |

ページ数 | 14 |

ジャーナル | Results in Mathematics |

巻 | 46 |

発行部数 | 3-4 |

DOI | |

出版物ステータス | Published - 2004 11 1 |

### Fingerprint

### ASJC Scopus subject areas

- Mathematics (miscellaneous)
- Applied Mathematics

### これを引用

**Algebraic independence of power series generated by linearly independent positive numbers.** / Tanaka, Takaaki.

研究成果: Article

*Results in Mathematics*, 巻. 46, 番号 3-4, pp. 367-380. https://doi.org/10.1007/BF03322889

}

TY - JOUR

T1 - Algebraic independence of power series generated by linearly independent positive numbers

AU - Tanaka, Takaaki

PY - 2004/11/1

Y1 - 2004/11/1

N2 - In this paper we establish, using Mahler’s method, the algebraic independence of the values at an algebraic number of power series closely related to decimal expansion of linearly independent positive numbers. First we consider a simpler case in Theorem 1 and then generalize it to Theorem 3, which includes Nishioka’s result quoted as Theorem 2 of this paper. Lemma 7 plays an essential role in the proof of Theorems 1 and 3.

AB - In this paper we establish, using Mahler’s method, the algebraic independence of the values at an algebraic number of power series closely related to decimal expansion of linearly independent positive numbers. First we consider a simpler case in Theorem 1 and then generalize it to Theorem 3, which includes Nishioka’s result quoted as Theorem 2 of this paper. Lemma 7 plays an essential role in the proof of Theorems 1 and 3.

KW - Algebraic independence

KW - Mahler’s method

UR - http://www.scopus.com/inward/record.url?scp=85043362830&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85043362830&partnerID=8YFLogxK

U2 - 10.1007/BF03322889

DO - 10.1007/BF03322889

M3 - Article

AN - SCOPUS:85043362830

VL - 46

SP - 367

EP - 380

JO - Results in Mathematics

JF - Results in Mathematics

SN - 1422-6383

IS - 3-4

ER -