The Poincaré series of the algebras of simultaneous invariants and covariants of two binary forms

摘要

Let I_(d1,d2) and C_(d1,d2) be the algebras of simultaneous invariants and simultaneous covariants of the two binary forms of degrees d_1 and d_2. Formulas for computation of the Poincaré series PI_(d1,d2)(z), PC_(d1,d2)(z) of the algebras are found. By using these formulas, we have computed the series for d_1, d_2 ≤ 20.