Irrationality Results for Values of Generalized Tschakaloff Series

Masaaki Amou, Masanori Katsurada

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2 Citations (Scopus)

Abstract

Arithmetical properties of values of the entire functionTq(x)=∑ n=0x n/q(1/2)n(n+1), whereqis a parameter, q>1, were first studied by L. Tschakaloff (1921,Math. Ann.80, 62-74;84, 100-114). In this paper we introduce a generalization ofTq(x), given by (1.3), and prove the irrationality results for the values of (1.3) at rational points (see Theorem and Corollaries at the end of Section 1). One of the essential tools in the proof is a variant of Mahler's transcendence method, due to J. H. Loxton and A. J. van der Poorten (1977,in"Transcendence Theory: Advances and Applications," pp. 211-226, Academic Press, San Diego).

Original languageEnglish
Pages (from-to)155-169
Number of pages15
JournalJournal of Number Theory
Volume77
Issue number1
DOIs
Publication statusPublished - 1999 Jul

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Irrationality
Transcendence
Series
Rational Points
Corollary
Entire
Theorem
Generalization

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Irrationality Results for Values of Generalized Tschakaloff Series. / Amou, Masaaki; Katsurada, Masanori.

In: Journal of Number Theory, Vol. 77, No. 1, 07.1999, p. 155-169.

Research output: Contribution to journalArticle

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