On a modularity conjecture of Andrews, Dixit, Schultz, and Yee for a variation of Ramanujan's \(\omega\)(\(q\))

DOI10.1016/j.aim.2017.12.002zbMath1386.11070arXiv1612.08219OpenAlexW2963024251WikidataQ123254308 ScholiaQ123254308MaRDI QIDQ1688640

Chris Jennings-Shaffer, Karl Mahlburg, Kathrin Bringmann

Publication date: 11 January 2018

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

Full work available at URL: https://arxiv.org/abs/1612.08219

zbMATH Keywords

mock theta functionsmodular formsinteger partitionsharmonic Maass formsAndrews' smallest parts functions

Mathematics Subject Classification ID

Forms of half-integer weight; nonholomorphic modular forms (11F37) Theta series; Weil representation; theta correspondences (11F27) Elementary theory of partitions (11P81)

Related Items (12)

On the number of parts in congruence classes for partitions into distinct parts ⋮ Rademacher expansions and the spectrum of 2d CFT ⋮ Distributions on partitions arising from Hilbert schemes and hook lengths ⋮ Linked partition ideals, directed graphs and \(q\)-multi-summations ⋮ Parity bias in partitions ⋮ Staircases to analytic sum-sides for many new integer partition identities of Rogers-Ramanujan type ⋮ BIASES IN INTEGER PARTITIONS ⋮ A simple proof of a congruence for a series involving the little \(q\)-Jacobi polynomials ⋮ A variant of \texttt{IdentityFinder} and some new identities of Rogers-Ramanujan-MacMahon type ⋮ Generating functions and congruences for some partition functions related to mock theta functions ⋮ Unimodal sequence generating functions arising from partition ranks ⋮ Uniform asymptotic formulas for the Fourier coefficients of the inverse of theta functions

Cites Work

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• The number of smallest parts in the partitions of n
• CONGRUENCES FOR ANDREWS' SMALLEST PARTS PARTITION FUNCTION AND NEW CONGRUENCES FOR DYSON'S RANK
• Congruences for the Andrews spt function
• Another smallest part function related to Andrews' spt function
• The Final Problem : An Account of the Mock Theta Functions
• Further Identities of the Rogers-Ramanujan Type

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