A note on Jacobians, Tutte polynomials, and two-variable zeta functions of graphs

We address questions posed by Lorenzini about relations between Jacobians, Tutte polynomials, and the Brill-Noether theory of finite graphs, as encoded in his two-variable zeta functions. In particular, we give examples showing that none of these invariants is determined by the other two.Comment: 9 pages, 6 figures. v2: Improved exposition, updated references. Final version, to appear in Exp. Mat