A note on the Poincar'e series of the invariants of ternary forms

TL;DR

This paper presents an analogue of Springer's formula for calculating the Poincaré series of the algebra invariants of ternary forms, advancing the understanding of their algebraic structure.

Contribution

It introduces a new formula analogous to Springer's for the Poincaré series of invariants of ternary forms, filling a gap in invariant theory.

Findings

Derived an explicit formula for the Poincaré series

Extended Springer's approach to ternary forms

Provided insights into the structure of algebra invariants

Abstract

Analogue of Springer's formula for the Poincar\'e series of the algebra invariants of ternary form is found.