### Abstract

Mahler's method gives algebraic independence results for the values of functions of several variables satisfying certain functional equations under the transformations of the variables represented as a kind of the multiplicative action of matrices with integral entries. In the Mahler's method, the entries of those matrices must be nonnegative; however, in the special case stated in this paper, one can admit those matrices to have a negative entry. We show the algebraic independence of the values of certain functions satisfying functional equations under the transformation represented by such matrices, expressing those values as linear combinations of the values of ordinary Mahler functions.

Original language | English |
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Pages (from-to) | 211-223 |

Number of pages | 13 |

Journal | Tokyo Journal of Mathematics |

Volume | 37 |

Issue number | 1 |

Publication status | Published - 2014 Jun 1 |

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### Keywords

- Algebraic independence
- Mahler's method

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**Arithmetic properties of solutions of certain functional equations with transformations represented by matrices including a negative entry.** / Tanaka, Takaaki.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Arithmetic properties of solutions of certain functional equations with transformations represented by matrices including a negative entry

AU - Tanaka, Takaaki

PY - 2014/6/1

Y1 - 2014/6/1

N2 - Mahler's method gives algebraic independence results for the values of functions of several variables satisfying certain functional equations under the transformations of the variables represented as a kind of the multiplicative action of matrices with integral entries. In the Mahler's method, the entries of those matrices must be nonnegative; however, in the special case stated in this paper, one can admit those matrices to have a negative entry. We show the algebraic independence of the values of certain functions satisfying functional equations under the transformation represented by such matrices, expressing those values as linear combinations of the values of ordinary Mahler functions.

AB - Mahler's method gives algebraic independence results for the values of functions of several variables satisfying certain functional equations under the transformations of the variables represented as a kind of the multiplicative action of matrices with integral entries. In the Mahler's method, the entries of those matrices must be nonnegative; however, in the special case stated in this paper, one can admit those matrices to have a negative entry. We show the algebraic independence of the values of certain functions satisfying functional equations under the transformation represented by such matrices, expressing those values as linear combinations of the values of ordinary Mahler functions.

KW - Algebraic independence

KW - Mahler's method

UR - http://www.scopus.com/inward/record.url?scp=84908062929&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84908062929&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84908062929

VL - 37

SP - 211

EP - 223

JO - Tokyo Journal of Mathematics

JF - Tokyo Journal of Mathematics

SN - 0387-3870

IS - 1

ER -