Comptes Rendus
Analyse et géométrie complexes
On the Erdős–Lax Inequality
Prasanna Kumar1
1 Department of Mathematics, Birla Institute of Technology and Science Pilani, K K Birla Goa Campus, Goa, India 403726
Comptes Rendus. Mathématique, Volume 360 (2022), pp. 1081-1085.

The Erdős–Lax Theorem states that if P(z)=∑ ν=1 n a ν z ν is a polynomial of degree n having no zeros in |z|<1, then

max |z|=1 |P ′ (z)|≤n 2max |z|=1 |P(z)|.

In this paper, we prove a sharpening of the above inequality (1). In order to prove our result we prove a sharpened form of the well-known Theorem of Laguerre on polynomials, which itself could be of independent interest.

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DOI : 10.5802/crmath.141
Classification : 30A10
Prasanna Kumar 1

1 Department of Mathematics, Birla Institute of Technology and Science Pilani, K K Birla Goa Campus, Goa, India 403726
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {On the {Erd\H{o}s{\textendash}Lax} {Inequality}},
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Prasanna Kumar. On the Erdős–Lax Inequality. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 1081-1085. doi : 10.5802/crmath.141. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.141/

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