Differentiability of Fourier Series related to Eisenstein series ( Please note date and time!)

In my talk, I will discuss the differentiability of Fourier Series of
the form

F_k(\tau)=\sum_{n=1}^{\infty}\sigma_{k-1}(n) n^{-k-1}e^{2\pi i n \tau} for k even.

These series are related to Eisenstein Series. Using modular (and
quasi-modular) properties of Eisenstein Series, we can find functional
equations for F_k, from which we can draw some conclusions on
differentiability of F_k. This approach was introduced by Itatsu in
1981 in a paper on Differentiability of Riemann's Function.

In the main part of my talk I will focus on the case when k=2. The
imaginary
part and the real part of F_2 exhibit different behaviour while
considering the
differentiability at both rational and irrational points. We find
that the differentiability of the imaginary part of F_2 at an irrational
point x depends
on the properties of the continued fraction expansion of x.

Then I will talk about the general case k even.