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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2401.01910 |
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| _version_ | 1866911767262658560 |
|---|---|
| author | Zhang, Ruiming |
| author_facet | Zhang, Ruiming |
| contents | In this work we prove that certain entire $q$-functions have infinitely many nonzero roots $\left\{ ρ_{n}\right\} _{n=1}^{\infty}$, as $n\to+\infty$ the moduli $\left|ρ_{n}\right|$ grow at least exponentially. Applications to entire $q$-functions defined by series expansions are provided. These functions include the $q$-analogue of the plane wave function $\mathcal{E}_{q}(z,t)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_01910 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Zeros of Certain Entire Functions Zhang, Ruiming Complex Variables In this work we prove that certain entire $q$-functions have infinitely many nonzero roots $\left\{ ρ_{n}\right\} _{n=1}^{\infty}$, as $n\to+\infty$ the moduli $\left|ρ_{n}\right|$ grow at least exponentially. Applications to entire $q$-functions defined by series expansions are provided. These functions include the $q$-analogue of the plane wave function $\mathcal{E}_{q}(z,t)$. |
| title | On the Zeros of Certain Entire Functions |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2401.01910 |