Note on the Roots of the Derivative of a Polynomial

Echols, W. H.

doi:10.1080/00029890.1920.11985956

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Real Polynomials1

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1929

2021

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Cited by 3 publications

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“…For integer m this is due to de Bruijn and Springer [1]. That same paper conjectured (5), which conjecture was open for about 50 years until the papers of Malamud and Pereira.…”

Section: ) Formentioning

confidence: 98%

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Critical points of polynomials

Тотик

2021

Acta Math. Hungar.

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This paper is devoted to the problem of where the critical points of a polynomial are relative to their zeros. Classical and new developments are surveyed along with illustrative examples. The paper finishes with a short proof of the sector theorem of Sendov and Sendov.This paper surveys some of the results regarding the location of the critical points of polynomials. A short proof will also be given for the beautiful recent sector theorem of B. Sendov and H. Sendov.The topic is very old, the most classical references are [30] by E. B. Van Vleck, [14] by M. Marden, [17] by Q. I. Rahman and G. Schmeisser and [24] by T. Sheil-Small. We shall however, also touch many newer developments that are not included in those works. We also mention the recent survey paper [21] by T. Richards that discusses some of the topics to be dealt with below.

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“…For integer m this is due to de Bruijn and Springer [1]. That same paper conjectured (5), which conjecture was open for about 50 years until the papers of Malamud and Pereira.…”

Section: ) Formentioning

confidence: 98%

“…The following simple proof is from [5]. Let z j± = a j ± ib j be a pair of complex conjugate roots and set z = x + iy.…”

Section: Real Polynomialsmentioning

confidence: 99%