On the problem of Kakeya
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911887479799808 |
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| author | Bakic, Rados |
| author_facet | Bakic, Rados |
| contents | We discuss a form of a well-known problem of Kakeya for complex polynomials. Let p(z) be a complex polynomial. This problem requires to find disc that contains n zeros of some derivative of p(z), provided that location of several zeros of p(z) is known. We find a disc that contains a zero of (k-1)-th derivative, if we know disc that contains k zeros of p(z). This result can be regarded as an extension of the Grace-Heawood theorem where k=2. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_16313 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the problem of Kakeya Bakic, Rados Complex Variables 26C10 (Primary) 30C15 (Secondary) We discuss a form of a well-known problem of Kakeya for complex polynomials. Let p(z) be a complex polynomial. This problem requires to find disc that contains n zeros of some derivative of p(z), provided that location of several zeros of p(z) is known. We find a disc that contains a zero of (k-1)-th derivative, if we know disc that contains k zeros of p(z). This result can be regarded as an extension of the Grace-Heawood theorem where k=2. |
| title | On the problem of Kakeya |
| topic | Complex Variables 26C10 (Primary) 30C15 (Secondary) |
| url | https://arxiv.org/abs/2405.16313 |