A Comparison Test for Meromorphic Extensions
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910183791263744 |
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| author | Glücksam, Adi Zou, Yuzhou Joey |
| author_facet | Glücksam, Adi Zou, Yuzhou Joey |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_05896 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Comparison Test for Meromorphic Extensions Glücksam, Adi Zou, Yuzhou Joey Complex Variables 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. |
| title | A Comparison Test for Meromorphic Extensions |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2601.05896 |