Author

J. Bannon

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Preprint Aug 2026

The prime spectrum of rings of integer-coefficient power series on the disk

This is a sequel to \cite{PaperI}, where it is shown that a discrete effective divisor on the open unit disk $\D$ is the zero divisor of a holomorphic function with integer Taylor coefficients if and only if it is invariant under complex conjugation. Building on that realization theorem and on the unit characterization...

J. Bannon, D. Feldman · 0 citations

Preprint Aug 2026

Weak Factorization and Product Systems Over Groupoids

We give a product-system description of generalized higher-rank graphs with the weak factorization property. For such a graph with degree-zero groupoid G, we prove that weak factorization is equivalent to multiplication inducing coherent bijections between balanced products of its homogeneous G-G-bisets. Consequently,...

J. Bannon, Alina Vdovina · 0 citations

Preprint Jul 2026

Non-isomorphism of rings of integer-coefficient holomorphic functions on disks of varying radius

For $\rho \in (0,1]$, let $R(\rho) = \mathbb{Z}[[z]] \cap O(B(0,\rho))$ denote the ring of power series with integer Taylor coefficients converging on the open disk $B(0,\rho)$. We prove that these rings are pairwise non-isomorphic as abstract rings. Three ingredients drive the proof: the ideal $(z)$ is the unique prin...

J. Bannon, D. Feldman · 0 citations