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PreprintCC BY 4.0arXiv

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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Cite

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BibTeX
@misc{banerjee2026jensenpólya,
  title = {{The Jensen--Pólya program and inequalities for arithmetic sequences}},
  author = {Koustav Banerjee and Kathrin Bringmann and Larry Rolen},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.14295},
  eprint = {2609.14295},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.14295},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The Jensen--Pólya program and inequalities for arithmetic sequences
AU  - Koustav Banerjee
AU  - Kathrin Bringmann
AU  - Larry Rolen
PY  - 2026
DA  - 2026/09/18
PB  - arXiv
DO  - 10.48550/arxiv.2609.14295
UR  - https://arxiv.org/abs/2609.14295
AB  - 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.
ER  -