Author

Chao Zu

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Preprint Aug 2026

Block Repetition of Numerical Invariants for the Submodules $[z^k-w^k]$ in $H^2(\mathbb D^2)$

For $k\ge 2$, let $M_k=[z^k-w^k]$ be the principal homogeneous submodule of the Hardy space over the bidisk. We determine Yang's complete sequence of numerical invariants and prove $$ \Sigma_0(M_k)=\frac{\pi^2}{6},\qquad \Sigma_j(M_k)=\Sigma_{\lceil j/k\rceil}([z-w]),\quad j\ge1. $$ The proof exploits a residue-class d...

Yin Liu, Yu-Feng Lu, Chao Zu · 1 citation

Preprint Aug 2026

Strict Monotonicity of Numerical Invariants for the Submodules $[(z-w)^k]$ in $H^2(\mathbb D^2)$

For $k\geq1$, let $M_k=[(z-w)^k]\subset H^2(\mathbb D^2)$. We first determine the banded Toeplitz matrices associated with the homogeneous components of $M_k$, together with explicit formulas for their determinants and the relevant algebraic cofactors. These formulas lead to a complete description of the spectrum of th...

Yin Liu, Yu-Feng Lu, Chao Zu · 1 citation