The Mordell integral, quantum modular forms, and mock Jacobi forms

DOI10.1007/S40993-015-0002-XzbMath1378.11058OpenAlexW1988312265WikidataQ59412303 ScholiaQ59412303MaRDI QIDQ680030

Robert C. Rhoades, Bobbie Chern

Publication date: 22 January 2018

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

Full work available at URL: https://doi.org/10.1007/s40993-015-0002-x

zbMATH Keywords

Jacobi formsRamanujanmock theta functionmock Jacobi formpartial theta functionMordell integralfalse theta functionpartial Jacobi theta function

Mathematics Subject Classification ID

(q)-calculus and related topics (05A30) Applications of the Hardy-Littlewood method (11P55) Discontinuous groups and automorphic forms (11F99) Jacobi forms (11F50)

Related Items (5)

Hecke-type triple sums associated with mock theta functions ⋮ Error functions, Mordell integrals and an integral analogue of a partial theta function ⋮ Asymptotic expansions, \(L\)-values and a new quantum modular form ⋮ On the perturbative expansion of exact bi-local correlators in JT gravity ⋮ A generalization of the Riemann-Siegel formula

Cites Work

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• On the dual nature of partial theta functions and Appell-Lerch sums
• The logistic-normal integral and its generalizations
• \(K3\) surfaces, \({\mathcal N}=4\) dyons and the Mathieu group \(M_{24}\)
• Superconformal algebras and mock theta functions. II: Rademacher expansion for \(K3\) surface
• Dyson's ranks and Maass forms
• Modular forms and quantum invariants of \(3\)-manifolds
• The definite integral \(\int_{-\infty}^\infty {e^{ax^2+bx}\over e^{cx+d}}dx\) and the analytic theory of numbers
• Partial theta functions and mock modular forms as \(q\)-hypergeometric series
• A unified approach to partial and mock theta functions
• Mock (false) theta functions as quantum invariants
• The \(f(q)\) mock theta function conjecture and partition ranks
• MOCK THETA FUNCTIONS AND QUANTUM MODULAR FORMS
• A Survey of Classical Mock Theta Functions
• Hecke-type double sums, Appell-Lerch sums, and mock theta functions, I
• Eulerian series as modular forms
• On the asymptotic behavior of Kac-Wakimoto characters
• Notes on the K3 Surface and the Mathieu GroupM₂₄
• Second Order Mock Theta Functions
• Computing the truncated theta function via Mordell integral
• A Convergent Series for the Partition Function p ( n )
• Vassiliev invariants and a strange identity related to the Dedekind eta-function

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