On the Poincaré series of the invariants of binary forms (Q802752)

A variation of a computation made by T. A. Springer which gives an explicit formula for the Poincaré series of binary forms is presented, and an algorithm for the computation of the Poincaré series is proposed. Using this algorithm, the authors compute some examples; this computation suggests the Dixmier conjecture: the ring of invariants of binary forms of degree 4i, \(i\geq 1\), contains a regular sequence \(f_ 2,...,f_{2n-1}\) with deg \(f_ k=k\). A possible candidate for this regular sequence is considered.