A remark concerning normal families and shared values
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918392767709184 |
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| author | Sauer, Andreas |
| author_facet | Sauer, Andreas |
| contents | We improve well-known results concerning normal families and shared values of meromorphic functions in the plane. In particular, we obtain two corollaries concerning meromorphic functions $f \colon {\mathbb C} \to {\widehat{\mathbb C}}$: i) If $f$ shares a non-zero finite value with $f'$, and such that $f'$ is bounded on the preimages of $f$ for a second value, then $f$ is normal. ii) If $f$ shares two finite values with $f'$, then $f$ and $f'$ are normal. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_00788 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A remark concerning normal families and shared values Sauer, Andreas Complex Variables 30D45 (Primary) 30D35 (Secondary) We improve well-known results concerning normal families and shared values of meromorphic functions in the plane. In particular, we obtain two corollaries concerning meromorphic functions $f \colon {\mathbb C} \to {\widehat{\mathbb C}}$: i) If $f$ shares a non-zero finite value with $f'$, and such that $f'$ is bounded on the preimages of $f$ for a second value, then $f$ is normal. ii) If $f$ shares two finite values with $f'$, then $f$ and $f'$ are normal. |
| title | A remark concerning normal families and shared values |
| topic | Complex Variables 30D45 (Primary) 30D35 (Secondary) |
| url | https://arxiv.org/abs/2509.00788 |