TY - JOUR

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

AU - Tanaka, Taka Aki

PY - 2005/6/1

Y1 - 2005/6/1

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].

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M3 - Article

AN - SCOPUS:24644484313

SN - 0030-6126

VL - 42

SP - 487

EP - 497

JO - Osaka Journal of Mathematics

JF - Osaka Journal of Mathematics

IS - 2

ER -