We give the characterization of the differentiability and nondifferentiability points of a generalization of the Riesz–Nágy–Takács (RNT) singular function, namely, the generalized RNT (GRNT) singular function. A particular characterization generalizes recent multifractal and metric-number-theoretical results associated with the RNT singular function. Furthermore, we compute the moments of the GRNT singular function.
"The derivative and moment of the generalized Riesz–Nágy–Takács function." Kyoto J. Math. 57 (1) 185 - 195, April 2017. https://doi.org/10.1215/21562261-3759567