On the rational approximation to Thue-Morse rational numbers

RENDICONTI DEL SEMINARIO MATEMATICO DELLA UNIVERSITA DI PADOVA（2024）

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摘要

Let b >= 2 and l >= 1 be integers. We establish that there is an absolute real number K such that all the partial quotients of the rational number Pi(l)(h=0)(1 - b(-2h)), of denominator b(2l+1 - 1), do not exceed exp(K(logb)(2 )root l2(l/2)).

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关键词

Rational approximation,continued fraction

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