On three third order mock theta functions and Hecke-type double sums

DOI10.1007/s11139-012-9376-8zbMath1284.11075arXiv1208.1330OpenAlexW3099450462MaRDI QIDQ1941052

Eric T. Mortenson

Publication date: 11 March 2013

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1208.1330

zbMATH Keywords

mock theta functionsAppell-Lerch sumsHecke-type double sumsindefinite theta series

Mathematics Subject Classification ID

Binomial coefficients; factorials; (q)-identities (11B65) Theta series; Weil representation; theta correspondences (11F27) Holomorphic modular forms of integral weight (11F11)

Related Items (22)

Some new mock theta functions ⋮ Bailey pairs and indefinite quadratic forms. II: False indefinite theta functions ⋮ On ranks and cranks of partitions modulo 4 and 8 ⋮ Three-parameter mock theta functions ⋮ ON FOUR NEW MOCK THETA FUNCTIONS ⋮ The Bailey chain and mock theta functions ⋮ Ramanujan's \(_1\psi_1\) summation, Hecke-type double sums, and Appell-Lerch sums ⋮ On the dual nature of partial theta functions and Appell-Lerch sums ⋮ Generalizations of mock theta functions and Appell-Lerch sums ⋮ Hecke-type double sums and mock theta functions ⋮ Several \(q\)-series transformation formulas and new Hecke-Rogers type series identities ⋮ PARTIAL INDEFINITE THETA IDENTITIES ⋮ Arithmetic properties of odd ranks and \(k\)-marked odd Durfee symbols ⋮ Parity of coefficients of mock theta functions ⋮ Universal mock theta functions and two-variable Hecke-Rogers identities ⋮ On second and eighth order mock theta functions ⋮ New mock theta conjectures. I ⋮ Four identities related to third-order mock theta functions ⋮ Third-order mock theta functions ⋮ Representations of mock theta functions ⋮ Unnamed Item ⋮ A proof of the mod 4 unimodal sequence conjectures and related mock theta functions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the modularity of the unified WRT invariants of certain Seifert manifolds
• \(q\)-orthogonal polynomials, Rogers-Ramanujan identities, and mock theta functions
• Infinite-dimensional Lie algebras, theta functions and modular forms
• A proof of the mock theta conjectures
• On the seventh order mock theta functions
• Hecke-type double sums, Appell-Lerch sums, and mock theta functions, I
• Hecke Modular Forms and the KAC-Peterson Identities
• The Fifth and Seventh Order Mock Theta Functions
• The Final Problem : An Account of the Mock Theta Functions
• Some Properties of Partitions

This page was built for publication: On three third order mock theta functions and Hecke-type double sums