The Erdős–Lax Theorem states that if is a polynomial of degree having no zeros in then
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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Prasanna Kumar 1
@article{CRMATH_2022__360_G9_1081_0, author = {Prasanna Kumar}, title = {On the {Erd\H{o}s{\textendash}Lax} {Inequality}}, journal = {Comptes Rendus. Math\'ematique}, pages = {1081--1085}, publisher = {Acad\'emie des sciences, Paris}, volume = {360}, year = {2022}, doi = {10.5802/crmath.141}, language = {en}, }
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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