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Schoenberg type inequalities

Schoenberg type inequalities

来源:Arxiv_logoArxiv
英文摘要

In the geometry of polynomials, Schoenberg's conjecture, now a theorem, is a quadratic inequality between the zeros and critical points of a polynomial whose zeros have their centroid at the origin. We call its generalizations to other orders Schoenberg type inequalities. While inequalities of order four have been previously established, little is known about other orders. In this paper, we present a Schoenberg type inequality of order six, as well as a novel inequality of order one, representing the first known result in the odd-order case. These results partially answer two open problems posed by Kushel and Tyaglov. We also make a connection to Sendov's conjecture.

Quanyu Tang

数学

Quanyu Tang.Schoenberg type inequalities[EB/OL].(2025-04-13)[2025-05-17].https://arxiv.org/abs/2504.09837.点此复制

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