2 problems

Let $\Omega$ be a convex domain and let $Z_\Omega(s)$ be its tropical zeta function. The image of the map $\Omega\mapsto Z_\Omega$ consists of functions holomorphic on $\Re(s)>1$.…

Higher-dimensional first-pole conjecture. The first pole occurs at this value, and its residue is proportional to the equiaffine surface volume of $\partial\Omega$.