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arXiv · 2609.14295

The Jensen--Pólya program and inequalities for arithmetic sequences

Koustav Banerjee·Kathrin Bringmann·Larry Rolen
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Abstract

We develop an analytic framework to study hyperbolicity of Jensen polynomials and related inequalities for arithmetic sequences with general asymptotic growth. Our results provide partial converses to the Hermite--Jensen phenomenon of Griffin, Ono, Zagier, and the third author. As applications we prove several conjectures concerning log-concavity, higher-order Turan inequalities, Laguerre inequalities, infinite log-concavity, and Toeplitz determinants for partition-type functions.

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Koustav Banerjee, Kathrin Bringmann, Larry Rolen. 2026-09-18. The Jensen--Pólya program and inequalities for arithmetic sequences. https://arxiv.org/abs/2609.14295

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