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

T. A. Tanaka

doi:10.1007/s00013-002-8237-x

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

T. A. Tanaka

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

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

Original language	English
Pages (from-to)	202-209
Number of pages	8
Journal	Archiv der Mathematik
Volume	78
Issue number	3
DOIs	https://doi.org/10.1007/s00013-002-8237-x
Publication status	Published - 2002 Mar 1

ASJC Scopus subject areas

Mathematics(all)

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10.1007/s00013-002-8237-x

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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.",

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

Abstract

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