Categorifying quadratic zeta functions
Jon Aycock, Andrew Kobin
TL;DR
This paper presents a categorification of the factorization of quadratic Dedekind zeta functions using objective linear algebra within the incidence algebra of the division poset, offering a new algebraic perspective.
Contribution
It introduces a novel categorification approach for quadratic zeta functions employing objective linear algebra in the incidence algebra framework.
Findings
Categorification of quadratic zeta function factorization
Application of objective linear algebra in incidence algebra
New algebraic perspective on zeta functions
Abstract
The Dedekind zeta function of a quadratic number field factors as a product of the Riemann zeta function and the -function of a quadratic Dirichlet character. We categorify this formula using objective linear algebra in the abstract incidence algebra of the division poset.
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Taxonomy
TopicsAdvanced Mathematical Identities · Commutative Algebra and Its Applications · Graph Labeling and Dimension Problems