Entire functions of several complex variables satisfying certain Fermat-type PDDEs
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866916543531581440 |
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| author | Xu, Hong Yan Mandal, Rajib Biswas, Raju |
| author_facet | Xu, Hong Yan Mandal, Rajib Biswas, Raju |
| contents | In this paper, we solve certain Fermat-type partial differential-difference equations for finite order entire functions of several complex variables. These results are significant generalizations of some earlier findings, especially those of Haldar and Ahamed (Entire solutions of several quadratic binomial and trinomial partial differential-difference equations in $\mathbb{C}^2$, Anal. Math. Phys., 12 (2022)). In addition, the results improve the previous results from the situation with two complex variables to the situation with several complex variables. To support our results, we have included several examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_19339 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Entire functions of several complex variables satisfying certain Fermat-type PDDEs Xu, Hong Yan Mandal, Rajib Biswas, Raju Complex Variables 39A45, 39A14, 39B32, 32W50, 30D35 In this paper, we solve certain Fermat-type partial differential-difference equations for finite order entire functions of several complex variables. These results are significant generalizations of some earlier findings, especially those of Haldar and Ahamed (Entire solutions of several quadratic binomial and trinomial partial differential-difference equations in $\mathbb{C}^2$, Anal. Math. Phys., 12 (2022)). In addition, the results improve the previous results from the situation with two complex variables to the situation with several complex variables. To support our results, we have included several examples. |
| title | Entire functions of several complex variables satisfying certain Fermat-type PDDEs |
| topic | Complex Variables 39A45, 39A14, 39B32, 32W50, 30D35 |
| url | https://arxiv.org/abs/2412.19339 |