Higher order Turán inequalities for the partition function

DOI10.1090/tran/7707zbMath1415.05020arXiv1706.10245OpenAlexW2964169188MaRDI QIDQ4967318

Larry X. W. Wang, William Y. C. Chen, Dennis X. Q. Jia

Publication date: 3 July 2019

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1706.10245

zbMATH Keywords

partition functionlog-concavityHardy-Ramanujan-Rademacher formulaJensen polynomialshigher-order Turán inequalities

Mathematics Subject Classification ID

Combinatorial inequalities (05A20) Analytic theory of partitions (11P82)

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Cites Work

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• Log-concavity of the partition function
• Jensen polynomials and the Turán and Laguerre inequalities
• Necessary and sufficient conditions and the Riemann hypothesis
• Infinite log-concavity: developments and conjectures
• Hermite polynomials
• Multiple positivity and the Riemann zeta-function
• On the generating functions of totally positive sequences. I
• Finite differences of the logarithm of the partition function
• Higher order Turán inequalities for the Riemann $\xi$-function
• Iterated sequences and the geometry of zeros
• Normalized Symmetric Functions, Newton's Inequalities, and a New Set of Stronger Inequalities
• The invariant theory of binary forms
• The Riemann Hypothesis and the Turan Inequalities
• Higher order Turán inequalities
• Integers, Polynomials, and Rings
• The spt-function of Andrews
• On polynomials, all of whose zeros are real
• A Convergent Series for the Partition Function p ( n )
• On the Series for the Partition Function
• On the Remainders and Convergence of the Series for the Partition Function
• On an inequality of P. Turán concerning Legendre polynomials
• Algorithms in invariant theory