Bivariate Poincare series for the algebra of covariants of a binary form

TL;DR

This paper derives a formula for the bivariate Poincaré series of the algebra of covariants associated with binary forms of degree d, providing a new tool for understanding their structure.

Contribution

The paper introduces a novel formula for computing the bivariate Poincaré series of covariants of binary forms, advancing algebraic invariant theory.

Findings

Derived an explicit formula for $\

$ ext{P}_d(z,t)$ for binary forms.

Facilitated calculations of covariant algebra structures.

Abstract

A formula for computation of the bivariate Poincar\'e series $\mathcal{P}_d(z,t)$ for the algebra of covariants of binary $d$-form is found.