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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.05896 |
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Table of Contents:
- 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.