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Zbl 1126.11036
Adamczewski, Boris; Bugeaud, Yann
Palindromic continued fractions. (English)
[J] Ann. Inst. Fourier 57, No. 5, 1557-1574 (2007). ISSN 0373-0956; ISSN 1777-5310/e

In this paper the authors investigate real numbers whose sequence of partial quotients enjoys some combinatorial properties involving the notion of palindrome. They provide three new transcendence criteria. The first criterion is stated that if the sequence of partial quotients begins in arbitrarily long palindromes, then the real number is either quadratic irrational or transcendental. The second and the third transcendental criteria assume that the sequence is not eventually periodic and include some bounded statements. The proofs depend upon the Schmidt's subspace theorem [{\it W. M. Schmidt}, Ann. Math. (2) 96, 526--551 (1972; Zbl 0226.10024)].
[Takao Komatsu (Hirosaki)]

MSC 2000:: *11J81 Transcendence (general theory)
11J70 Continued fractions and generalizations
68R15 Combinatorics on words

Keywords: continued fractions; palindromes; transcendental numbers; subspace theorem

Citations: Zbl 0226.10024

Cited in: Zbl 1123.11023

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