Extensions of MacMahon's sums of divisors

DOI10.1007/s40687-024-00421-6arXiv2309.03191OpenAlexW4391531466WikidataQ128661316 ScholiaQ128661316MaRDI QIDQ6202880

George E. Andrews, Roberto Tauraso, Tewodoros Amdeberhane

Publication date: 27 February 2024

Published in: Research in the Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2309.03191

zbMATH Keywords

quasi-modular forms\(q\)-harmonic sumsgeneralized sums of divisors

Mathematics Subject Classification ID

Partitions; congruences and congruential restrictions (11P83) Forms of half-integer weight; nonholomorphic modular forms (11F37) Multiple Dirichlet series and zeta functions and multizeta values (11M32)

Cites Work

• The algebra of generating functions for multiple divisor sums and applications to multiple zeta values
• A \(q\)-analog of a general rational sum identity
• On a general \(q\)-identity
• The algebra of bi-brackets and regularized multiple Eisenstein series
• Quasi-modularity of generalized sum-of-divisors functions
• Zeta stars
• Some \(q\)-series identities related to divisor functions
• On \(q\)-analogues of two-one formulas for multiple harmonic sums and multiple zeta star values
• q-Series Arising From The Study of Random Graphs
• MacMahon's sum-of-divisors functions, Chebyshev polynomials, and quasi-modular forms
• New properties of multiple harmonic sums modulo 𝑝 and 𝑝-analogues of Leshchiner’s series
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