\(r\)-log-concavity of partition functions

DOI10.1007/s11139-017-9975-5zbMath1407.05016OpenAlexW2793491475MaRDI QIDQ1733367

Qing-Hu Hou, Zuo-Ru Zhang

Publication date: 21 March 2019

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11139-017-9975-5

zbMATH Keywords

partition functionHardy-Ramanujan-Rademacher formula\(r\)-log-concavity

Mathematics Subject Classification ID

Combinatorial aspects of partitions of integers (05A17) Asymptotic results on arithmetic functions (11N37) Elementary theory of partitions (11P81)

Related Items (9)

Laguerre inequalities for discrete sequences ⋮ Inequalities for the overpartition function arising from determinants ⋮ Higher order log-concavity of the overpartition function and its consequences ⋮ Log-concavity of the restricted partition function \(p_{\mathcal{A}}(n, k)\) and the new Bessenrodt-Ono type inequality ⋮ An inequality for coefficients of the real-rooted polynomials ⋮ Determinantal inequalities for the partition function ⋮ On a new class of Laguerre-Pólya type functions with applications in number theory ⋮ SOME OBSERVATIONS AND SPECULATIONS ON PARTITIONS INTO d-TH POWERS ⋮ Positivity of the determinants of the partition function and the overpartition function

Cites Work

• Log-concavity of the partition function
• Asymptotic \(r\)-log-convexity and P-recursive sequences
• Finite differences of the logarithm of the partition function
• ON A SEQUENCE INVOLVING SUMS OF PRIMES
• The 2-log-convexity of the Apéry Numbers
• On the Series for the Partition Function
• On the Remainders and Convergence of the Series for the Partition Function

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