### Abstract

In this paper we establish algebraic independence of the values of a certain infinite product as well as its all successive derivatives at algebraic points other than its zeroes, using the fact that the logarithmic derivative of an infinite product gives a partial fraction expansion. Such an infinite product is generated by a linear recurrence. The method used for proving the algebraic independence is based on the theory of Mahler functions of several variables.

Original language | English |
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Title of host publication | AIP Conference Proceedings |

Pages | 116-123 |

Number of pages | 8 |

Volume | 1385 |

DOIs | |

Publication status | Published - 2011 |

Event | Diophantine Analysis and Related Fields 2011, DARF - 2011 - Musashino, Tokyo, Japan Duration: 2011 Mar 3 → 2011 Mar 5 |

### Other

Other | Diophantine Analysis and Related Fields 2011, DARF - 2011 |
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Country | Japan |

City | Musashino, Tokyo |

Period | 11/3/3 → 11/3/5 |

### Fingerprint

### Keywords

- Algebraic independence
- infinite products
- Mahler's method

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*AIP Conference Proceedings*(Vol. 1385, pp. 116-123) https://doi.org/10.1063/1.3630047

**Algebraic independence properties related to certain infinite products.** / Tanaka, Takaaki.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*AIP Conference Proceedings.*vol. 1385, pp. 116-123, Diophantine Analysis and Related Fields 2011, DARF - 2011, Musashino, Tokyo, Japan, 11/3/3. https://doi.org/10.1063/1.3630047

}

TY - GEN

T1 - Algebraic independence properties related to certain infinite products

AU - Tanaka, Takaaki

PY - 2011

Y1 - 2011

N2 - In this paper we establish algebraic independence of the values of a certain infinite product as well as its all successive derivatives at algebraic points other than its zeroes, using the fact that the logarithmic derivative of an infinite product gives a partial fraction expansion. Such an infinite product is generated by a linear recurrence. The method used for proving the algebraic independence is based on the theory of Mahler functions of several variables.

AB - In this paper we establish algebraic independence of the values of a certain infinite product as well as its all successive derivatives at algebraic points other than its zeroes, using the fact that the logarithmic derivative of an infinite product gives a partial fraction expansion. Such an infinite product is generated by a linear recurrence. The method used for proving the algebraic independence is based on the theory of Mahler functions of several variables.

KW - Algebraic independence

KW - infinite products

KW - Mahler's method

UR - http://www.scopus.com/inward/record.url?scp=81755188356&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=81755188356&partnerID=8YFLogxK

U2 - 10.1063/1.3630047

DO - 10.1063/1.3630047

M3 - Conference contribution

SN - 9780735409477

VL - 1385

SP - 116

EP - 123

BT - AIP Conference Proceedings

ER -