Fine Regularity of Minkowski’s Question-Mark Function and Its Generalizations

This poster presents results on the pointwise regularity and multifractal structure of the Minkowski question-mark function M, together with a generalized family of functions F_B obtained by replacing the dyadic structure with an arbitrary base B > 1. Using oscillation-based Hölder regularity, continued-fraction dynamics, and thermodynamic formalism on the Gauss shift, we derive an explicit formula for the pointwise Hölder exponent of M at irrational points, prove infinite smoothness at rationals, and obtain the multifractal spectrum via a variational principle. We also characterize the continuity of F_B, which holds only in the classical case B = 2.