# On the derivative of the Minkowski question mark function ?(x)

@article{Dushistova2007OnTD, title={On the derivative of the Minkowski question mark function ?(x)}, author={Anna Aleksandrovna Dushistova and Nikolai Germanovich Moshchevitin}, journal={Journal of Mathematical Sciences}, year={2007}, volume={182}, pages={463-471} }

Let x = [0; a1, a2, …] be the regular continued fraction expansion of an irrational number x ∈ [0, 1]. For the derivative of the Minkowski function ?(x) we prove that ?′(x) = +∞, provided that $ \mathop {{\lim \sup }}\limits_{t \to \infty } \frac{{{a_1} + \cdots + {a_t}}}{t} < {\kappa_1} = \frac{{2\log {\lambda_1}}}{{\log 2}} = {1.388^{+} } $, and ?′(x) = 0, provided that $ \mathop {{\lim \inf }}\limits_{t \to \infty } \frac{{{a_1} + \cdots + {a_t}}}{t} > {\kappa_2} = \frac{{4{L_5} - 5{L_4…

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