## Osaka Journal of Mathematics

- Osaka J. Math.
- Volume 42, Number 2 (2005), 487-497.

### Algebraic independence of the values of power series, Lambert series, and infinite products generated by linear recurrences

#### 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].

#### Article information

**Source**

Osaka J. Math., Volume 42, Number 2 (2005), 487-497.

**Dates**

First available in Project Euclid: 21 July 2006

**Permanent link to this document**

https://projecteuclid.org/euclid.ojm/1153494390

**Mathematical Reviews number (MathSciNet)**

MR2147737

**Zentralblatt MATH identifier**

1119.11041

#### Citation

Tanaka, Taka-aki. Algebraic independence of the values of power series, Lambert series, and infinite products generated by linear recurrences. Osaka J. Math. 42 (2005), no. 2, 487--497. https://projecteuclid.org/euclid.ojm/1153494390