Multifractal analysis of Thomae’s function

In 1875, K. J. Thomae introduced a function that is continuous on the set of irrational numbers and discontinuous on the set of rational numbers. Among its many intriguing properties, Thomae’s function is notably non-differentiable at all irrational points. In this paper, we rigorously determine its pointwise regularity at every point and compute its Hölder spectrum.