Poincare series of the multigraded algebras of <i>SL </i>₂-invariants

Abstract

Formulas for computation of the multivariate Poincare series $\mathcal{P}(\mathcal{C}_{d}, z_1, z_2,..., z_n,t)$ and $\mathcal{P}(\mathcal{I}_{d}, z_1, z_2,..., z_n)$, are found, where $\mathcal{C}_{d}, \mathcal{I}_{d}, \;\; {d} = (d_1, d_2,..., d_n)$ are multigraded algebras of joint covariants and joint invariants for n binary forms of degrees $d_1, d_2,..., d_n $.