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

Autor: Taka Aki Tanaka
Rok vydání: 2002
Předmět:
Zdroj: Archiv der Mathematik. 78:202-209
ISSN: 1420-8938
0003-889X
DOI: 10.1007/s00013-002-8237-x
Popis: Transcendence of the number \( \sum_{k=0}^\infty \alpha^{r_k} \), where \( \alpha \) is an algebraic number with 0 1 and \( \{r_k\}_{k\geqq0} \) is a sequence of positive integers such that \( \lim_{k\to\infty}\, r_{k+1}/r_k = d \in \mathbb{N}\, \backslash \{1\} \), is proved by Mahler's method. This result implies the transcendence of the number \( \sum_{k=0}^\infty \alpha^{kd^k} \).
Databáze: OpenAIRE
Externí odkaz: