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arXiv · 2601.05896

A Comparison Test for Meromorphic Extensions

Adi Glücksam·Yuzhou Joey Zou
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Abstract

We provide a comparison test for meromorphic extensions, i.e., if two series are ``close enough" then the existence of a meromorphic extension of one to the entire complex plane ensures a similar extension for the other. We use this result to generate new examples of Dirichlet series admitting meromorphic extensions. Moreover, we demonstrate that our requirements are optimal by constructing a collection of counterexamples where the series are ``close but not enough": one series admits a meromorphic extension while the other possesses a natural boundary.

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Adi Glücksam, Yuzhou Joey Zou. 2026-01-09. A Comparison Test for Meromorphic Extensions. https://arxiv.org/abs/2601.05896

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