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On the Log-Concavity of the D'Arcais Polynomials for Normalised Functions

2026/07/16 by Johann Stumpenhusen
#math.NT

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Abstract

A sequence (an)n ∈ ℕ of non-negative real numbers is called log-concave at n if an2 ≥ an+1an-1. This property has been generalised in various ways to families of polynomials. We introduce a new variant and show that certain types of D'Arcais polynomials have the respective properties at certain points.

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