Zeros of Harmonic Functions whose Caustic is a Non-Singular Image of an Epicycloid
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909730803286016 |
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| author | Sampson, Eli |
| author_facet | Sampson, Eli |
| contents | Recent researchers have investigated how the zeros of certain families of complex harmonic functions change with a single parameter. Many leverage the well-behaved images of the critical curve and the harmonic analogue of the Argument Principle to prove zero-counting theorems. In this paper, we investigate the zeros of a family of harmonic functions for which the image of its critical curve is a non-singular linear image of an epicycloid. By analyzing this curve and using the harmonic analogue of the Argument Principle, we obtain a detailed zero-counting theorem for our family. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_06724 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Zeros of Harmonic Functions whose Caustic is a Non-Singular Image of an Epicycloid Sampson, Eli Complex Variables Recent researchers have investigated how the zeros of certain families of complex harmonic functions change with a single parameter. Many leverage the well-behaved images of the critical curve and the harmonic analogue of the Argument Principle to prove zero-counting theorems. In this paper, we investigate the zeros of a family of harmonic functions for which the image of its critical curve is a non-singular linear image of an epicycloid. By analyzing this curve and using the harmonic analogue of the Argument Principle, we obtain a detailed zero-counting theorem for our family. |
| title | Zeros of Harmonic Functions whose Caustic is a Non-Singular Image of an Epicycloid |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2508.06724 |