Families of quasimodular forms and Jacobi forms: The crank statistic for partitions
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Publication:4911542
DOI10.1090/S0002-9939-2012-11383-8zbMath1276.11167arXiv1106.1866MaRDI QIDQ4911542
Publication date: 19 March 2013
Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1106.1866
Combinatorial aspects of partitions of integers (05A17) Applications of the Hardy-Littlewood method (11P55) Partitions; congruences and congruential restrictions (11P83) Analytic theory of partitions (11P82) Partition identities; identities of Rogers-Ramanujan type (11P84)
Related Items (4)
The first positive rank and crank moments for overpartitions ⋮ Integer partitions, probabilities and quantum modular forms ⋮ The crank moments weighted by the parity of cranks ⋮ Asymptotics of crank generating functions and Ramanujan congruences
Cites Work
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- Higher order spt-functions
- The theory of Jacobi forms
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- Partitions weighted by the parity of the crank
- Periods of modular forms and Jacobi theta functions
- Relations between the ranks and cranks of partitions
- The ranks and cranks of partitions moduli 2, 3, and 4
- The \(f(q)\) mock theta function conjecture and partition ranks
- Taylor coefficients of mock-Jacobi forms and moments of partition statistics
- New Combinatorial Interpretations of Ramanujan's Partition Congruences Mod 5,7 and 11
- Dyson’s crank of a partition
- MacMahon's sum-of-divisors functions, Chebyshev polynomials, and quasi-modular forms
- Asymptotics for rank and crank moments
- Partition congruences and the Andrews-Garvan-Dyson crank
- CONGRUENCES FOR THE COEFFICIENTS OF WEAKLY HOLOMORPHIC MODULAR FORMS
- Partition Statistics and Quasiharmonic Maass Forms
- Some Properties of Partitions
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