Egerváry's theorems for harmonic trinomials
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | |
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| _version_ | 1866917653204959232 |
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| author | Barrera, Gerardo Barrera, Waldemar Navarrete, Juan Pablo |
| author_facet | Barrera, Gerardo Barrera, Waldemar Navarrete, Juan Pablo |
| contents | In this manuscript, we study the arrangements of the roots in the complex plane for the lacunary harmonic polynomials called harmonic trinomials. We provide necessary and sufficient conditions so that two general harmonic trinomials have the same set of roots up to a rotation around the origin in the complex plane, a reflection over the real axis, or a composition of the previous both transformations. This extends the results of J. Egerváry 1930 for the setting of trinomials to the setting of harmonic trinomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_01720 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Egerváry's theorems for harmonic trinomials Barrera, Gerardo Barrera, Waldemar Navarrete, Juan Pablo Classical Analysis and ODEs Complex Variables 12D10, 30C15, 26C10, 30C10 In this manuscript, we study the arrangements of the roots in the complex plane for the lacunary harmonic polynomials called harmonic trinomials. We provide necessary and sufficient conditions so that two general harmonic trinomials have the same set of roots up to a rotation around the origin in the complex plane, a reflection over the real axis, or a composition of the previous both transformations. This extends the results of J. Egerváry 1930 for the setting of trinomials to the setting of harmonic trinomials. |
| title | Egerváry's theorems for harmonic trinomials |
| topic | Classical Analysis and ODEs Complex Variables 12D10, 30C15, 26C10, 30C10 |
| url | https://arxiv.org/abs/2307.01720 |