MacMahon's sum-of-divisors functions, Chebyshev polynomials, and quasi-modular forms

DOI10.1515/CRELLE.2011.179zbMath1337.11002arXiv1010.5769OpenAlexW2964030008MaRDI QIDQ4914031

Simon C. F. Rose, George E. Andrews

Publication date: 17 April 2013

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1010.5769

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Holomorphic modular forms of integral weight (11F11) Arithmetic functions; related numbers; inversion formulas (11A25)

Related Items (14)

The algebra of generating functions for multiple divisor sums and applications to multiple zeta values ⋮ Tropical mirror symmetry for elliptic curves ⋮ The number of tagged parts over the partitions with designated summands ⋮ Unnamed Item ⋮ Modular anomaly equation for Schur index of \(\mathcal{N} = 4\) super-Yang-Mills ⋮ Quasi-modularity of generalized sum-of-divisors functions ⋮ Extensions of MacMahon's sums of divisors ⋮ Higher order spt-functions ⋮ \(\mathcal{N} = 2^\ast\) Schur indices ⋮ Multiple Eisenstein Series and q-Analogues of Multiple Zeta Values ⋮ Arithmetic properties of bipartitions with designated summands ⋮ Families of quasimodular forms and Jacobi forms: The crank statistic for partitions ⋮ On the number of partitions with designated summands ⋮ Arithmetic properties of partitions with designated summands

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