A new approach to the Dyson rank conjectures

DOI10.1007/s11139-021-00530-8zbMath1525.11120arXiv2012.06676OpenAlexW4210301711WikidataQ122959171 ScholiaQ122959171MaRDI QIDQ6098228

Frank G. Garvan

Publication date: 13 June 2023

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

Full work available at URL: https://arxiv.org/abs/2012.06676

zbMATH Keywords

Ramanujan partition congruencesHecke-Rogers seriesDyson's rank conjectures

Mathematics Subject Classification ID

Combinatorial aspects of partitions of integers (05A17) Partitions; congruences and congruential restrictions (11P83) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Congruences for modular and (p)-adic modular forms (11F33) Elementary theory of partitions (11P81) Partition identities; identities of Rogers-Ramanujan type (11P84)

Related Items (1)

Properties of the Appell-Lerch function (I)

Cites Work

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• Exotic Bailey-Slater spt-functions. I: Group A.
• Dyson's ranks and Appell-Lerch sums
• Some observations on Dyson's new symmetries of partitions
• Properties of the Appell-Lerch function (I)
• Universal mock theta functions and two-variable Hecke-Rogers identities
• Rank and conjugation for the Frobenius representation of an overpartition
• Hecke-type double sums, Appell-Lerch sums, and mock theta functions, I
• Hecke Modular Forms and the KAC-Peterson Identities
• The Fifth and Seventh Order Mock Theta Functions
• New Combinatorial Interpretations of Ramanujan's Partition Congruences Mod 5,7 and 11
• Dyson’s crank of a partition
• Affine Lie algebras and Hecke modular forms
• Applications of Basic Hypergeometric Functions
• Transformation properties for Dyson’s rank function
• Some Properties of Partitions
• Ramanujan's Lost Notebook

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