Title: Eisenstein series twisted Shintani zeta function

Abstrct:

In this talk, we introduce the zeta function of the prehomogenous vector space of binary cubic forms, twisted by the real analytic Eisenstein series.  We sketch the proof of the meromorphic continuation of this zeta function and identify its poles and their residues. This zeta function can be used to prove the equidistribution of the lattice shape of cubic rings.