Identities and inequalities for the \(M_2\)-rank of partitions without repeated odd parts modulo 8

DOI10.1007/S11139-021-00486-9zbMath1501.11095OpenAlexW3198435418MaRDI QIDQ2155876

Xiang Zhao, Ernest X. W. Xia

Publication date: 15 July 2022

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

Full work available at URL: https://doi.org/10.1007/s11139-021-00486-9

zbMATH Keywords

mock theta functions\(M_2\)-rankpartitions without repeated odd partsAppell-Lerch sumsDyson's rank

Mathematics Subject Classification ID

Combinatorial aspects of partitions of integers (05A17) Partitions; congruences and congruential restrictions (11P83) Theta series; Weil representation; theta correspondences (11F27) Elementary theory of partitions (11P81)

Related Items (1)

Inequalities for the \(M_2\)-rank modulo 12 of partitions without repeated odd parts

Cites Work

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• On the dual nature of partial theta functions and Appell-Lerch sums
• Dyson's ranks and Appell-Lerch sums
• The generating functions of the rank and crank modulo 8
• \(M_2\)-rank differences for partitions without repeated odd parts
• On ranks and cranks of partitions modulo 4 and 8
• Some observations on Dyson's new symmetries of partitions
• The \(M_{2}\)-rank of partitions without repeated odd parts modulo 6 and 10
• Overpartitions, lattice paths, and Rogers-Ramanujan identities
• Two theorems of Gauss and allied identities proved arithmetically
• Hecke-type double sums, Appell-Lerch sums, and mock theta functions, I
• On the Rank and the Crank Modulo 4 and 8
• Some Eighth Order Mock Theta Functions
• Second Order Mock Theta Functions
• A Generalization of the Gollnitz-Gordon Partition Theorems
• Some Properties of Partitions

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