On the Problem of Kakeya

Let $$p(z)$$ be a complex polynomial of degree $$n$$, having $$k$$ of its zeros in the unit disc. We prove that at least one zero of $$p^{(k-1)}(z)$$ lies in the disc $$|z|\le \frac{2(n-k+1)}{\ln 2} $$.

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Publication Details

Journal
Proceedings of the Bulgarian Academy of Sciences
Published
2025-05-28
DOI
https://doi.org/10.7546/crabs.2025.05.01
Primary Topic
Probability and Risk Models
Type
article
Field-Weighted Citation Impact
0.00
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article

On the Problem of Kakeya

Radoš Bakić
Proceedings of the Bulgarian Academy of Sciences
Probability and Risk Models
article

On the Problem of Kakeya

Radoš Bakić
article en

Abstract

Let $$p(z)$$ be a complex polynomial of degree $$n$$, having $$k$$ of its zeros in the unit disc. We prove that at least one zero of $$p^{(k-1)}(z)$$ lies in the disc $$|z|\le \frac{2(n-k+1)}{\ln 2} $$.

Proceedings of the Bulgarian Academy of SciencesVol. 78(5)
University of Belgrade (RS)
Openalex Percentile: Top 87%
Probability and Risk Models
DOIOpen Access PDFOpenAlex
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On the Problem of Kakeya — Radoš Bakić · Proceedings of the Bulgarian Academy of Sciences (2025) | TGRS Research Map | TGRS