On the explicit construction of higher deformations of partition statistics

DOI10.1215/00127094-2008-035zbMath1154.11034arXiv0707.1717OpenAlexW2016881381MaRDI QIDQ939643

Kathrin Bringmann

Publication date: 28 August 2008

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0707.1717

zbMATH Keywords

congruencescircle methodsmallest parts functionrank momentsweak Maass formsDurfee symbolsquasimock theta functions

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Forms of half-integer weight; nonholomorphic modular forms (11F37) Analytic theory of partitions (11P82)

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The first positive rank and crank moments for overpartitions, Secord-order cusp forms and mixed mock modular forms, \(\ell\)-adic properties of partition functions, Higher Siegel theta lifts on Lorentzian lattices, harmonic Maass forms, and Eichler-Selberg type relations, Overpartition ranks and quantum modular forms, Exotic Bailey-Slater spt-functions. I: Group A., An analogue of $k$-marked Durfee symbols for strongly unimodal sequences, Taylor coefficients of mock-Jacobi forms and moments of partition statistics, Effective estimates for the smallest parts function, Inequalities between ranks and cranks, Theta lifts for Lorentzian lattices and coefficients of mock theta functions, THE ASYMPTOTIC DISTRIBUTION OF TRACES OF WEAK MAASS FORMS, Asymptotics, Turán inequalities, and the distribution of the BG-rank and 2-quotient rank of partitions, On a modularity conjecture of Andrews, Dixit, Schultz, and Yee for a variation of Ramanujan's \(\omega\)(\(q\)), Asymptotic formulas for spt-crank of partitions, The asymptotic distribution of Andrews' smallest parts function, Mixed Rademacher and BPS black holes, On spt-crank-type functions, Asymptotic equidistribution for partition statistics and topological invariants, Algebraic and transcendental formulas for the smallest parts function, Explicit congruences for \(k\)-marked Durfee symbols, Higher order spt-functions, \(\ell \)-adic properties of smallest parts functions, Zagier-type dualities and lifting maps for harmonic Maass-Jacobi forms, Arithmetic properties of odd ranks and \(k\)-marked odd Durfee symbols, Quantum Modular Forms and Singular Combinatorial Series with Distinct Roots of Unity, Quantum modular forms and singular combinatorial series with repeated roots of unity, CONGRUENCES FOR ANDREWS' SMALLEST PARTS PARTITION FUNCTION AND NEW CONGRUENCES FOR DYSON'S RANK, Asymptotic inequalities for positive crank and rank moments, Congruences for the Andrews spt function, Congruences for a mock modular form on \(\mathrm{SL}_2(\mathbb{Z})\) and the smallest parts function, HECKE-TYPE CONGRUENCES FOR ANDREWS' SPT-FUNCTION MODULO 16 AND 32, ASYMPTOTICS FOR MOMENTS OF HIGHER RANKS, Euler-like recurrences for smallest parts functions, Universal mock theta functions and two-variable Hecke-Rogers identities, On Ramanujan’s definition of mock theta function, The nonholomorphic parts of certain weak Maass forms, Algebraic relations between partition functions and the \(j\)-function, A polyharmonic Maass form of depth 3/2 for \(\mathrm{SL}_2(\mathbb{Z})\), The combinatorics of $k$-marked Durfee symbols, Notes on the \(spt\) function of George E. Andrews, SYMMETRY OF k-MARKED DURFEE SYMBOLS, q-series and weight 3/2 Maass forms, Rank and crank moments for overpartitions, Effective bounds for the Andrews spt-function, Taylor coefficients of non-holomorphic Jacobi forms and applications, Mock modular Eisenstein series with Nebentypus, Congruences for Andrews’ spt-Function Modulo 32760 and Extension of Atkin’s Hecke-Type Partition Congruences, Congruences for Andrews’ spt-function modulo powers of $5$, $7$ and $13$, A proof of the mod 4 unimodal sequence conjectures and related mock theta functions, Moments of ranks and cranks, and quotients of Eisenstein series and the Dedekind eta function, On a completed generating function of locally harmonic Maass forms, Asymptotics of higher order ospt-functions for overpartitions

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