On the Hausdorff dimension of Riemann’s non-differentiable function

Recent findings show that the classical Riemann's non-differentiable function has a physical and geometric nature as irregular trajectory of polygonal vortex filament driven by binormal flow. In this article, we give an upper estimate its Hausdorff dimension. We also adapt result to multifractal setting. To prove these results, recalculate asymptotic behavior around rationals from novel perspective, underlining connections with Talbot effect Gauss sums, hope it is useful lower bound dimension answer further questions.