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

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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 languageEnglish
Pages (from-to)487-497
Number of pages11
JournalOsaka Journal of Mathematics
Volume42
Issue number2
Publication statusPublished - 2005 Jun

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Lambert Series
Algebraic Independence
Linear Recurrence
Infinite product
Power series
Theorem
Necessary Conditions
Dependent
Sufficient Conditions

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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title = "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].",
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