Universality of the Epstein zeta-function in the lattice aspect

We will talk about recent joint work with A. Södergren where we show that the Epstein zeta-function is universal in the Lattice-aspect. In particular let $f$ be an analytic function in the strip $\{s:1/2 < \Re s<1\}$ which is real valued for real $s$. Then for any compact set $K \subset \{s:1/2< \Re s <1\}$, real number $\varepsilon>0$ and for any sufficiently large $n$ there exists some $n$-dimensional lattice $L$ such that
$$ \max_{s \in K} \biggl|\,2^{s-1}V_{n}^{-s}E_{n}\left(L,{{ns}\over 2}\right)\,-\,f(s)\biggr|\,<\,\varepsilon, $$
where $E_{n}(L,s)$ denotes the Epstein zeta-function associated with the lattice $L$ and $V_{n}=\pi^{n/2}/\,\Gamma(n/2+1)$ is the volume of the $n$-dimensional sphere. If we allow a difference of two Epstein zeta-functions (with different lattices) to approximate the function rather than a single Epstein zeta-function the same result holds in the full half plane $\Re s>1/2$. This is the first case of a Voronin type universality theorem that also holds in the half plane of absolute convergence.
The main ingredients in our proof are results on statistics of lengths of lattice vectors from Södergren's thesis and some approximation lemmas of Dirichlet polynomials.