Asymptotics for rank partition functions

DOI10.1090/S0002-9947-09-04553-XzbMath1189.11049arXiv0708.0691OpenAlexW2131027334MaRDI QIDQ3631863

Kathrin Bringmann

Publication date: 22 June 2009

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0708.0691

zbMATH Keywords

partitionsmock theta functionsrank of a partitionweak Maass forms

Mathematics Subject Classification ID

Combinatorial aspects of partitions of integers (05A17) Forms of half-integer weight; nonholomorphic modular forms (11F37) Analytic theory of partitions (11P82)

Related Items

Higher depth mock theta functions and \(q\)-hypergeometric series ⋮ Asymptotic equidistribution and convexity for partition ranks ⋮ Coefficients of Harmonic Maass Forms ⋮ Inequalities between overpartition ranks for all moduli ⋮ Biases among classes of rank-crank partitions (mod 11) ⋮ Inequalities for ranks of partitions and the first moment of ranks and cranks of partitions ⋮ Inequalities for full rank differences of 2-marked Durfee symbols ⋮ A short proof of the Mock Theta Conjectures using Maass forms ⋮ Asymptotics for \(q\)-expansions involving partial theta functions ⋮ Mock modular forms as $p$-adic modular forms ⋮ On the explicit construction of higher deformations of partition statistics ⋮ Dyson's partition ranks and their multiplicative extensions ⋮ Partitions, Durfee symbols, and the Atkin-Garvan moments of ranks ⋮ Asymptotic formulas related to the \(M_2\)-rank of partitions without repeated odd parts ⋮ On the asymptotic behavior of Kac-Wakimoto characters ⋮ On a sign pattern for the crank function of cubic partition pairs ⋮ Monotonicity properties for ranks of overpartitions ⋮ Arithmetic properties of non-harmonic weak Maass forms ⋮ Asymptotics of crank generating functions and Ramanujan congruences ⋮ On certain explicit congruences for mock theta functions ⋮ Ranks of overpartitions: asymptotics and inequalities

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Dyson's ranks and Maass forms
• Generalization of Dyson's rank and non-Rogers-Ramanujan partitions
• The ranks of partitions modulo 2
• Modular transformations of Ramanujan's fifth and seventh order mock theta functions
• The ranks and cranks of partitions moduli 2, 3, and 4
• The \(f(q)\) mock theta function conjecture and partition ranks
• Some Asymptotic Formulae for the Mock Theta Series of Ramanujan
• Some Properties of Partitions