A uniqueness problem concerning entire functions and their derivatives
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2022
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866929286173163520 |
|---|---|
| author | Sauer, Andreas Schweizer, Andreas |
| author_facet | Sauer, Andreas Schweizer, Andreas |
| contents | We determine all entire functions $f$ such that for nonzero complex values $a\neq b$ the implications $f=a \Rightarrow f' =a$ and $f' =b \Rightarrow f=b$ hold. This solves an open problem in uniqueness theory. In this context we give a normality criterion, which might be interesting in its own right. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_11341 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A uniqueness problem concerning entire functions and their derivatives Sauer, Andreas Schweizer, Andreas Complex Variables 30D35 (primary), 30D45 (secondary) We determine all entire functions $f$ such that for nonzero complex values $a\neq b$ the implications $f=a \Rightarrow f' =a$ and $f' =b \Rightarrow f=b$ hold. This solves an open problem in uniqueness theory. In this context we give a normality criterion, which might be interesting in its own right. |
| title | A uniqueness problem concerning entire functions and their derivatives |
| topic | Complex Variables 30D35 (primary), 30D45 (secondary) |
| url | https://arxiv.org/abs/2208.11341 |