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摘要
For beta %26gt; 1, a .)beta maps each infinite word a(1)a(2)... is an element of N-N to a real number Sigma(infinity)(i=1) alpha(i)/beta(i). We define Xi(alpha, beta) by (s(alpha,0)(1))(beta) where s(alpha,0)(1) is a lexicographically greatest mechanical word of slope alpha. This paper demonstrates that the function Xi enjoys devil%26apos;s staircaselike properties. Its continuity, partial and total differentiability will be investigated. We also present a set of Xi-values, in which any finite number of members are algebraically independent over the field of rationals.
- 出版日期2013-11
