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 Derivative of the Riesz-N{\'a}gy-Tak{\'a}cs function Bull. Korean Math. Soc. 2011 Vol. 48, No. 2, 261-275 https://doi.org/10.4134/BKMS.2011.48.2.261Printed March 1, 2011 In-Soo Baek Pusan University of Foreign Studies Abstract : We give characterizations of the differentiability points and the non-differentiability points of the Riesz-N{\'a}gy-Tak{\'a}cs(RNT) singular function using the distribution sets in the unit interval. Using characterizations, we show that the Hausdorff dimension of the non-differentiability points of the RNT singular function is greater than $0$ and the packing dimension of the infinite derivative points of the RNT singular function is less than $1$. Further the RNT singular function is nowhere differentiable in the sense of topological magnitude, which leads to that the packing dimension of the non-differentiability points of the RNT singular function is 1. Finally we show that our characterizations generalize a recent result from the $(\tau, \tau -1)$-expansion associated with the RNT singular function adding a new result for a sufficient condition for the non-differentiability points. Keywords : Hausdorff dimension, packing dimension, distribution set, local dimension set, singular function, metric number theory MSC numbers : 26A30, 28A80 Downloads: Full-text PDF