### Abstract

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.

Original language | English |
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Pages (from-to) | 367-380 |

Number of pages | 14 |

Journal | Results in Mathematics |

Volume | 46 |

Issue number | 3-4 |

DOIs | |

Publication status | Published - 2004 Nov 1 |

### Fingerprint

### Keywords

- Algebraic independence
- Mahler’s method

### ASJC Scopus subject areas

- Mathematics (miscellaneous)
- Applied Mathematics

### Cite this

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

Research output: Contribution to journal › Article

*Results in Mathematics*, vol. 46, no. 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

VL - 46

SP - 367

EP - 380

JO - Results in Mathematics

JF - Results in Mathematics

SN - 1422-6383

IS - 3-4

ER -