On the number of odd values of the Klein \(j\)-function and the cubic partition function

DOI10.1016/j.jnt.2014.12.022zbMath1323.11085arXiv1409.6271OpenAlexW1975078322WikidataQ114157492 ScholiaQ114157492MaRDI QIDQ2257316

Fabrizio Zanello

Publication date: 24 February 2015

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

Full work available at URL: https://arxiv.org/abs/1409.6271

zbMATH Keywords

four-square theoremmodular forms modulo 2density odd valuesbinary \(q\)-seriescubic partition functionKlein \(j\)-functionsum-of-divisor function

Mathematics Subject Classification ID

Combinatorial aspects of partitions of integers (05A17) Asymptotic results on arithmetic functions (11N37) Partitions; congruences and congruential restrictions (11P83) Modular and automorphic functions (11F03) Congruences for modular and (p)-adic modular forms (11F33)

Related Items (5)

On the density of the odd values of the partition function. II: An infinite conjectural framework ⋮ Deducing the positive odd density of \(p(n)\) from that of a multipartition function: an unconditional proof ⋮ On the density of the odd values of the partition function and the \(t\)-multipartition function ⋮ On the density of the odd values of the partition function ⋮ Nonzero coefficients of half-integral weight modular forms mod \(\ell \)

Cites Work

• Parity of the coefficients of modular forms
• The nilpotence order of the mod 2 Hecke operators
• A new lower bound on the number of odd values of the ordinary partition function
• A mod \(\ell\) Atkin-Lehner theorem and applications
• Distribution of parity of the partition function in arithmetic progressions
• Parity of the partition function
• Divisibilite de certaines fonctions arithmétiques
• On the parity of additive representation functions
• RECIPROCALS OF BINARY POWER SERIES
• ON THE PARITY OF PARTITION FUNCTIONS
• Parity of the coefficients of Klein’s $j$-function
• On the Distribution of Parity in the Partition Function
• Ramanujan's Lost Notebook
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