A Comparison Test for Meromorphic Extensions
Complex Variables
2026-05-04 v2
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.
Cite
@article{arxiv.2601.05896,
title = {A Comparison Test for Meromorphic Extensions},
author = {Adi Glücksam and Yuzhou Joey Zou},
journal= {arXiv preprint arXiv:2601.05896},
year = {2026}
}