Abstract
In this paper we prove that the Turán inequality in quaternionic setting holds for all polynomials of degree \(n\le 2\) and for some particular subclasses of polynomials of arbitrary degree \(n\ge 3\). It is important to note that the proofs of Turán’s inequality in the complex case do not work in the quaternionic setting for \(n\ge 3\), however we are lead to make the intriguing conjecture that the Turán inequality still holds for all quaternionic polynomials of arbitrary degree \(n\ge 3\).
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The authors thank the anonymous referees for their comments on how to shorten the proofs of Theorems 2.1 and 3.1.
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Communicated by Rafał Abłamowicz
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Gal, S.G., Sabadini, I. On the Turán Inequality for Quaternionic Polynomials. Adv. Appl. Clifford Algebras 29, 78 (2019). https://doi.org/10.1007/s00006-019-0997-5
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DOI: https://doi.org/10.1007/s00006-019-0997-5