Moments of ranks and cranks, and quotients of Eisenstein series and the Dedekind eta function

DOI10.1016/j.jnt.2022.04.014OpenAlexW2941244820WikidataQ114156490 ScholiaQ114156490MaRDI QIDQ2079493

Liuquan Wang, Yifan Yang

Publication date: 30 September 2022

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.00361

zbMATH Keywords

partitionsEisenstein seriesrankscranksquasi-modular formssmallest parts functionsrank and crank moments

Mathematics Subject Classification ID

Combinatorial aspects of partitions of integers (05A17) Partitions; congruences and congruential restrictions (11P83) Forms of half-integer weight; nonholomorphic modular forms (11F37) Modular and automorphic functions (11F03) Congruences for modular and (p)-adic modular forms (11F33) Holomorphic modular forms of integral weight (11F11)

Related Items (1)

Explicit congruences for \(k\)-marked Durfee symbols

Cites Work

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• Higher order spt-functions
• \(\ell \)-adic properties of smallest parts functions
• On the explicit construction of higher deformations of partition statistics
• Partitions, Durfee symbols, and the Atkin-Garvan moments of ranks
• Relations between the ranks and cranks of partitions
• The odd moments of ranks and cranks
• Mappings and symmetries of partitions
• Congruences for Andrews’ spt-function modulo powers of $5$, $7$ and $13$
• The number of smallest parts in the partitions of n
• CONGRUENCES FOR ANDREWS' SMALLEST PARTS PARTITION FUNCTION AND NEW CONGRUENCES FOR DYSON'S RANK
• Vanishing of modular forms at infinity
• Ramanujan congruences for p_-k (mod 11')
• Dyson’s crank of a partition
• Congruences for the Andrews spt function
• The spt-function of Andrews
• Partition Statistics and Quasiharmonic Maass Forms
• Some Properties of p(n) and c(n) Modulo Powers of 13
• Proof of a conjecture of Ramanujan
• On the Zeros of Eisenstein Series
• Ramanujans Vermutung über Zerfällungszahlen.
• Further Congruence Properties of the Fourier Coefficients of the Modular Invariant j(τ)
• Some Properties of Partitions

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