``Strange combinatorial quantum modular forms

DOI10.1016/j.jnt.2016.06.005zbMath1348.11043OpenAlexW2501055553MaRDI QIDQ311480

Caleb Ki, Yen Nhi Truong Vu, Bowen Yang, Amanda Folsom

Publication date: 13 September 2016

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jnt.2016.06.005

zbMATH Keywords

\(q\)-seriesmodular forms\(q\)-hypergeometric seriesbasic hypergeometric seriesquantum modular formsstrongly unimodal sequencesunimodal sequences

Mathematics Subject Classification ID

Forms of half-integer weight; nonholomorphic modular forms (11F37) Generalized hypergeometric series, ({}_pF_q) (33C20) Applications of basic hypergeometric functions (33D90)

Related Items (15)

Jacobi’s triple product, mock theta functions, unimodal sequences and the q-bracket ⋮ Quantum Jacobi forms and finite evaluations of unimodal rank generating functions ⋮ Periodic partial theta functions and \(q\)-hypergeometric knot multisums as quantum Jacobi forms ⋮ RANK GENERATING FUNCTIONS FOR ODD-BALANCED UNIMODAL SEQUENCES, QUANTUM JACOBI FORMS, AND MOCK JACOBI FORMS ⋮ Quantum Jacobi forms and balanced unimodal sequences ⋮ Quantum modular forms and singular combinatorial series with repeated roots of unity ⋮ Quantum mock modular forms arising from eta-theta functions ⋮ A family of vector-valued quantum modular forms of depth two ⋮ Quantum Jacobi forms and sums of tails identities ⋮ Universal mock theta functions as quantum Jacobi forms ⋮ Quantum Jacobi forms in number theory, topology, and mathematical physics ⋮ Asymptotics and Ramanujan's mock theta functions: then and now ⋮ Peak positions of strongly unimodal sequences ⋮ A short note on higher Mordell integrals ⋮ Asymptotic expansions, partial theta functions, and radial limit differences of mock modular and modular forms

Uses Software

• DLMF

Cites Work

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• A ``strange vector-valued quantum modular form
• Cyclotomic completions of polynomial rings
• Half-integral weight Eichler integrals and quantum modular forms
• q-identities for Maass waveforms
• Modular forms and quantum invariants of \(3\)-manifolds
• Unimodal sequences and ``strange functions: a family of quantum modular forms
• Integer partitions, probabilities and quantum modular forms
• On modular forms of half integral weight
• MOCK THETA FUNCTIONS AND QUANTUM MODULAR FORMS
• Dyson’s crank of a partition
• Vassiliev invariants and a strange identity related to the Dedekind eta-function

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