Congruences for the Andrews spt function

DOI10.1073/pnas.1015339107zbMath1286.11168OpenAlexW1966138439WikidataQ34490426 ScholiaQ34490426MaRDI QIDQ4907454

Ken Ono

Publication date: 2 February 2013

Published in: Proceedings of the National Academy of Sciences (Search for Journal in Brave)

Full work available at URL: https://europepmc.org/articles/pmc3021019

zbMATH Keywords

Ramanujan-type congruencesAndrews \(\text{spt}(n)\) partition functionharmonic Maaß\ forms

Mathematics Subject Classification ID

Partitions; congruences and congruential restrictions (11P83) Congruences for modular and (p)-adic modular forms (11F33) Hecke-Petersson operators, differential operators (one variable) (11F25)

Related Items (19)

\(\ell\)-adic properties of partition functions ⋮ Nonholomorphic Ramanujan-type congruences for Hurwitz class numbers ⋮ Congruences for \(\overline{\operatorname{spt}}_\omega(n)\) modulo powers of primes ⋮ Effective estimates for the smallest parts function ⋮ On a modularity conjecture of Andrews, Dixit, Schultz, and Yee for a variation of Ramanujan's \(\omega\)(\(q\)) ⋮ The asymptotic distribution of Andrews' smallest parts function ⋮ Algebraic and transcendental formulas for the smallest parts function ⋮ Higher order spt-functions ⋮ \(\ell \)-adic properties of smallest parts functions ⋮ Proof of the Andrews-Dyson-Rhoades conjecture on the spt-crank ⋮ 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 ⋮ HECKE-TYPE CONGRUENCES FOR TWO SMALLEST PARTS FUNCTIONS ⋮ Algebraic relations between partition functions and the \(j\)-function ⋮ Legendre theorems for subclasses of overpartitions ⋮ 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 $13$ ⋮ Moments of ranks and cranks, and quotients of Eisenstein series and the Dedekind eta function

Cites Work

• On the explicit construction of higher deformations of partition statistics
• Dyson's ranks and Maass forms
• Distribution of the partition function modulo composite integers \(M\)
• On two geometric theta lifts
• Distribution of the partition function modulo \(m\)
• q-series and weight 3/2 Maass forms
• Congruence properties for the partition function
• ON THE NUMBER OF SOLUTIONS TO CERTAIN DIAGONAL EQUATIONS OVER FINITE FIELDS

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