  Riemann's non-differentiable function is one of the most famous examples of
continuous but nowhere differentiable functions, but it has also been shown to
be relevant from a physical point of view. Indeed, it satisfies the
Frisch-Parisi multifractal formalism, which establishes a relationship with
turbulence and implies some intermittent nature. It also plays a surprising
role as a physical trajectory in the evolution of regular polygonal vortices
that follow the binormal flow. With this motivation, we focus on one more
classic tool to measure intermittency, namely the fourth-order flatness, and we
refine the results that can be deduced from the multifractal analysis to show
that it diverges logarithmically. We approach the problem in two ways: with
structure functions in the physical space and with high-pass filters in the
Fourier space.
