On the problem of Kakeya

Rados Bakic

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arXiv · 2405.16313

On the problem of Kakeya

Rados Bakic

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Abstract

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.

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Rados Bakic. 2024-05-25. On the problem of Kakeya. https://arxiv.org/abs/2405.16313

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