Log-concavity for partitions without sequences

Lukas Mauth

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arXiv · 2306.07459

Log-concavity for partitions without sequences

Lukas Mauth

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Abstract

We prove log-concavity for the function counting partitions without sequences. We use an exact formula for a mixed-mock modular form of weight zero, explicit estimates on modified Kloosterman sums and analytic techniques. Finally, we establish the higher Tur\'an inequalities in an asymptotic form of the aforementioned partition function using a well established criterion of Griffin, Ono, Rolen, and Zagier on the zeros of Jensen polynomials.

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Lukas Mauth. 2023-06-12. Log-concavity for partitions without sequences. https://arxiv.org/abs/2306.07459

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