### Abstract

In this paper we establish algebraic independence criteria for the values at an algebraic point of Mahler functions each of which satisfies either a multiplicative type of functional equation or an additive one. As application we construct, using a linear recurrence sequence, an entire function defined by an infinite product such that its values as well as its all successive derivatives at algebraic points other than its zeroes are algebraically independent. Zeroes of such an entire function form a subsequence of the linear recurrence sequence. We prove the algebraic independency by reducing those values at algebraic points to those of Mahler functions.

Original language | English |
---|---|

Pages (from-to) | 77-104 |

Number of pages | 28 |

Journal | Monatshefte fur Mathematik |

Volume | 174 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2014 |

### Fingerprint

### Keywords

- Algebraic independence
- Infinite products
- Mahler functions

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Monatshefte fur Mathematik*,

*174*(1), 77-104. https://doi.org/10.1007/s00605-014-0617-3

**Algebraic independence results for the values of certain Mahler functions and their application to infinite products.** / Kurosawa, Takeshi; Tachiya, Yohei; Tanaka, Takaaki.

Research output: Contribution to journal › Article

*Monatshefte fur Mathematik*, vol. 174, no. 1, pp. 77-104. https://doi.org/10.1007/s00605-014-0617-3

}

TY - JOUR

T1 - Algebraic independence results for the values of certain Mahler functions and their application to infinite products

AU - Kurosawa, Takeshi

AU - Tachiya, Yohei

AU - Tanaka, Takaaki

PY - 2014

Y1 - 2014

N2 - In this paper we establish algebraic independence criteria for the values at an algebraic point of Mahler functions each of which satisfies either a multiplicative type of functional equation or an additive one. As application we construct, using a linear recurrence sequence, an entire function defined by an infinite product such that its values as well as its all successive derivatives at algebraic points other than its zeroes are algebraically independent. Zeroes of such an entire function form a subsequence of the linear recurrence sequence. We prove the algebraic independency by reducing those values at algebraic points to those of Mahler functions.

AB - In this paper we establish algebraic independence criteria for the values at an algebraic point of Mahler functions each of which satisfies either a multiplicative type of functional equation or an additive one. As application we construct, using a linear recurrence sequence, an entire function defined by an infinite product such that its values as well as its all successive derivatives at algebraic points other than its zeroes are algebraically independent. Zeroes of such an entire function form a subsequence of the linear recurrence sequence. We prove the algebraic independency by reducing those values at algebraic points to those of Mahler functions.

KW - Algebraic independence

KW - Infinite products

KW - Mahler functions

UR - http://www.scopus.com/inward/record.url?scp=84898541094&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84898541094&partnerID=8YFLogxK

U2 - 10.1007/s00605-014-0617-3

DO - 10.1007/s00605-014-0617-3

M3 - Article

AN - SCOPUS:84898541094

VL - 174

SP - 77

EP - 104

JO - Monatshefte fur Mathematik

JF - Monatshefte fur Mathematik

SN - 0026-9255

IS - 1

ER -