MacMahon's sums-of-divisors and allied \(q\)-series

DOI10.1016/J.AIM.2024.109820MaRDI QIDQ6608719

Ken Ono, Ajit Singh, T. Amdeberhan

Publication date: 20 September 2024

Published in: Advances in Mathematics (Search for Journal in Brave)

zbMATH Keywords

partitionsquasimodular formsdivisor functions

Mathematics Subject Classification ID

Modular and automorphic functions (11F03) Other Dirichlet series and zeta functions (11M41) Congruences for modular and (p)-adic modular forms (11F33) Holomorphic modular forms of integral weight (11F11) Jacobi forms (11F50) Arithmetic functions; related numbers; inversion formulas (11A25)

Cites Work

• Higher order spt-functions
• Quasi-modularity of generalized sum-of-divisors functions
• The Nekrasov-Okounkov hook length formula: refinement, elementary proof, extension and applications
• Divisibilite de certaines fonctions arithmétiques
• Relations between the ranks and cranks of partitions
• Divisors of numbers and their continuations in the theory of partitions.
• Kombinatorische Anzahlbestimmungen für Gruppen, Graphen und chemische Verbindungen.
• Triple product identity, Quintuple product identity and Ramanujan’s differential equations for the classical Eisenstein series
• Ramanujan congruences for p_-k (mod 11')
• MacMahon's sum-of-divisors functions, Chebyshev polynomials, and quasi-modular forms
• Extensions of MacMahon's sums of divisors
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