Transcendence of the values of certain series with Hadamard's gaps

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Abstract

Transcendence of the number ∑k=0 αrk, where α is an algebraic number with 0 < |α| < 1 and {rk}k≧0 is a sequence of positive integers such that limk→∞ rk+1/rk = d ∈ ℕ / {1}, is proved by Mahler's method. This result implies the transcendence of the number ∑k=0 αkdk.

Original languageEnglish
Pages (from-to)202-209
Number of pages8
JournalArchiv der Mathematik
Volume78
Issue number3
DOIs
Publication statusPublished - 2002 Mar 1

ASJC Scopus subject areas

  • Mathematics(all)

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