The f(q) mock theta function conjecture and partition ranks

2006/01/30 by Kathrin Bringmann, Ken Ono · 30 citations
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #Asymptotic formula #Combinatorics #Conjecture #Function (biology) #Holomorphic function #Integer (computer science) #Mathematics #Partition (number theory) #Partition function (quantum field theory) #Pure mathematics #Ramanujan theta function #Ramanujan's sum #Rank (graph theory) #Theta function

paper · doi:10.1007/s00222-005-0493-5

openalex publication_date 2006/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/25

Citations

• Tenth order mock theta functions in Ramanujan's Lost Notebook
• On Modular Forms of Half Integral Weight

Cited by

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• Hecke-type double sums, Appell-Lerch sums, and mock theta functions (I)
• New polar-finite forms of generalized Euler identities for A₁⁽¹⁾-string functions and mock theta conjecture-like identities
• Heegner divisors, L-functions and harmonic weak Maass forms
• Period Relations, Jacobi Forms and Eichler Integral
• Congruences modulo powers of 5 for the rank parity function
• Locally harmonic Maass forms and the kernel of the Shintani lift
• Properties of Lerch Sums and Ramanujan's Mock Theta Functions
• Rademacher-type exact formula and higher order Turán inequalities for cubic overpartitions
• Singular invariants and coefficients of weak harmonic Maass forms of weight 5/2
• Transcendental formulas for the coefficients of Ramanujan's mock theta functions
• Inequalities for full rank differences of 2-marked Durfee symbols
• On the explicit construction of higher deformations of partition statistics
• c_{\rm eff} from Resurgence at the Stokes Line
• Theta liftings on weak Maass forms
• Asymptotics for rank partition functions
• Computation of harmonic weak Maass forms
• Joyce invariants for K3 surfaces and mock theta functions
• Weierstrass mock modular forms and elliptic curves
• Faber polynomials and Poincaré series
• Partitions weighted by the parity of the crank
• On certain explicit congruences for mock theta functions
• Generalized modular forms including the weak Maass forms,the Ramanujan's Theta functions and the Tau function
• On the positivity of black hole degeneracies in string theory
• Weak harmonic Maass forms of weight 5/2 and a mock modular form for the partition function
• Superconformal algebras and mock theta functions
• Proof of the umbral moonshine conjecture
• N=2 Superconformal Algebra and the Entropy of Calabi–Yau Manifolds