4 problems

Let $X$ be an integral regular projective curve of genus $g$ over ${\Bbb F}_q$. The rank $n$ non-abelian zeta function $\zeta_{X/{\Bbb F}_q,n}(s)$ is the zeta function associated w…

Let $X/{\mathbb F}_q$ be an integral regular projective curve, and let $\zeta_{X,{\mathbb F}_q;n}(s)$ denote its rank $n$ zeta function, defined through the generating function of…

Let the moduli space of rank $n$ semistable lattices carry its universal family of tori, and let the associated infinite-dimensional Hilbert bundle have the smooth sections paramet…

Let $X$ be a curve over $\bF_q$. For rank $r$, write $\what\zeta_{X,r}(s)=\what Z_{X,r}(q^{-rs})$ for the non-abelian zeta function of rank-$r$ semistable bundles, and let…