Entire functions with an arithmetic sequence of exponents
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929449441689600 |
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| author | Ruth, Dallas Tran, Khang |
| author_facet | Ruth, Dallas Tran, Khang |
| contents | For a given entire function $f(z)=\sum_{j=0}^{\infty}a_{j}z^{j}$, we study the zero distribution of $f_{r}(z)=\sum_{j\equiv r\pmod m}a_{j}z^{j}$ where $m\in\mathbb{N}$ and $0\le r<m$. We find conditions under which the zeros of $f_{r}(z)$ lie on $m$ radial rays defined by $\Im z^{m}=0$ and $\Re z^{m}\le0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_02096 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Entire functions with an arithmetic sequence of exponents Ruth, Dallas Tran, Khang Complex Variables 30C15, 26C10, 11C08 For a given entire function $f(z)=\sum_{j=0}^{\infty}a_{j}z^{j}$, we study the zero distribution of $f_{r}(z)=\sum_{j\equiv r\pmod m}a_{j}z^{j}$ where $m\in\mathbb{N}$ and $0\le r<m$. We find conditions under which the zeros of $f_{r}(z)$ lie on $m$ radial rays defined by $\Im z^{m}=0$ and $\Re z^{m}\le0$. |
| title | Entire functions with an arithmetic sequence of exponents |
| topic | Complex Variables 30C15, 26C10, 11C08 |
| url | https://arxiv.org/abs/2408.02096 |