The sharp constant in the Mashreghi--Ransford inequality [r-libre/4270]

Bouthat, Ludovick ORCID: https://orcid.org/0000-0002-2094-3028, Mashreghi, Javad et Morneau-Guérin, Frédéric ORCID: https://orcid.org/0000-0001-7610-4648 (02 oct. 2026). The sharp constant in the Mashreghi--Ransford inequality. Communication (sur invitation) présentée au CUNY GC Harmonic Analysis and PDE Seminar, New York.

Fichier(s) associé(s) à ce document :

PDF - mashreghi_ransford_talk.pdf
Contenu du fichier : Diaporama

Catégorie de document :	Communications à des congrès/colloques et conférences (non publiées)
Évaluation par un comité de lecture :	Non
Étape de publication :	Non publié
Résumé :	Let a sub n be a sequence of complex numbers. Consider its two binomial transforms, defined by summing the terms a sub k against the binomial coefficients, with and without alternating signs. Let beta be greater than one, and let alpha be the square root of beta squared minus one. Assume that both binomial transforms grow at most exponentially at rate beta to the n. In 2005, Mashreghi and Ransford proved an inequality controlling the asymptotic growth of a sub n at rate alpha to the n in terms of the corresponding asymptotic growth rates of the two binomial transforms. Their result involved a universal constant kappa, which they showed to lie between two divided by the square root of three and two. We prove that the optimal value of kappa is exactly two divided by the square root of three. Our proof uses exponential generating functions, Phragmén–Lindelöf estimates, and Cauchy’s formula, and we compare it with the original argument of Mashreghi and Ransford.
Déposant:	Morneau-Guérin, Frédéric
Responsable :	Frédéric Morneau-Guérin
Dépôt :	08 oct. 2026 12:52
Dernière modification :	08 oct. 2026 12:52

RÉVISER