### Abstract

In Theorem 1 of this paper, we establish the necessary and sufficient condition for the values of a power series, a Lambert series, and an infinite product generated by a linear recurrence at the same set of algebraic points to be algebraically dependent. In Theorem 4, from which Theorems 1-3 are deduced, we obtain an easily confirmable condition under which the values more general than those considered in Theorem 1 are algebraically independent, improving the method of [5].

Original language | English |
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Pages (from-to) | 487-497 |

Number of pages | 11 |

Journal | Osaka Journal of Mathematics |

Volume | 42 |

Issue number | 2 |

Publication status | Published - 2005 Jun |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**Algebraic independence of the values of power series, lambert series, and infinite products generated by linear recurrences.** / Tanaka, Takaaki.

Research output: Contribution to journal › Article

*Osaka Journal of Mathematics*, vol. 42, no. 2, pp. 487-497.

}

TY - JOUR

T1 - Algebraic independence of the values of power series, lambert series, and infinite products generated by linear recurrences

AU - Tanaka, Takaaki

PY - 2005/6

Y1 - 2005/6

N2 - In Theorem 1 of this paper, we establish the necessary and sufficient condition for the values of a power series, a Lambert series, and an infinite product generated by a linear recurrence at the same set of algebraic points to be algebraically dependent. In Theorem 4, from which Theorems 1-3 are deduced, we obtain an easily confirmable condition under which the values more general than those considered in Theorem 1 are algebraically independent, improving the method of [5].

AB - In Theorem 1 of this paper, we establish the necessary and sufficient condition for the values of a power series, a Lambert series, and an infinite product generated by a linear recurrence at the same set of algebraic points to be algebraically dependent. In Theorem 4, from which Theorems 1-3 are deduced, we obtain an easily confirmable condition under which the values more general than those considered in Theorem 1 are algebraically independent, improving the method of [5].

UR - http://www.scopus.com/inward/record.url?scp=24644484313&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=24644484313&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:24644484313

VL - 42

SP - 487

EP - 497

JO - Osaka Journal of Mathematics

JF - Osaka Journal of Mathematics

SN - 0030-6126

IS - 2

ER -