Congruences for Andrews’ spt-Function Modulo 32760 and Extension of Atkin’s Hecke-Type Partition Congruences

DOI10.1007/978-1-4614-6642-0_8zbMath1286.11164arXiv1011.1957OpenAlexW2162072870MaRDI QIDQ2840797

Frank G. Garvan

Publication date: 23 July 2013

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1011.1957

zbMATH Keywords

partitionscongruencesmodular formsweak Maass formsAndrews's spt-function

Mathematics Subject Classification ID

Partitions; congruences and congruential restrictions (11P83) Forms of half-integer weight; nonholomorphic modular forms (11F37) Congruences for modular and (p)-adic modular forms (11F33) Analytic theory of partitions (11P82)

Related Items (3)

\(\ell \)-adic properties of smallest parts functions ⋮ HECKE-TYPE CONGRUENCES FOR ANDREWS' SPT-FUNCTION MODULO 16 AND 32 ⋮ A proof of the mod 4 unimodal sequence conjectures and related mock theta functions

Cites Work

• Unnamed Item
• The partition function and Hecke operators
• \(\ell \)-adic properties of smallest parts functions
• On the explicit construction of higher deformations of partition statistics
• Rank and crank moments for overpartitions
• Relations between the ranks and cranks of partitions
• Congruences for Andrews’ spt-function modulo powers of $5$, $7$ and $13$
• Automorphic Properties of Generating Functions for Generalized Rank Moments and Durfee Symbols
• The number of smallest parts in the partitions of n
• CONGRUENCES FOR ANDREWS' SMALLEST PARTS PARTITION FUNCTION AND NEW CONGRUENCES FOR DYSON'S RANK
• The determination of Gauss sums
• Multiplicative Congruence Properties and Density Problems for p(n)
• Congruences for the Andrews spt function
• Ramanujan Congruences for p_-k(n)

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