no. G9
Analyse et géométrie complexes
On the Erdős–Lax Inequality
Kumar, Prasanna1
1 Department of Mathematics, Birla Institute of Technology and Science Pilani, K K Birla Goa Campus, Goa, India 403726
Comptes Rendus. Mathématique, Tome 360 (2022) no. G9, 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
Kumar, Prasanna 1

1 Department of Mathematics, Birla Institute of Technology and Science Pilani, K K Birla Goa Campus, Goa, India 403726 
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Kumar, Prasanna. On the Erdős–Lax Inequality. Comptes Rendus. Mathématique, Tome 360 (2022) no. G9, pp. 1081-1085. doi : 10.5802/crmath.141. http://www.numdam.org/articles/10.5802/crmath.141/

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