ARITHMETIC OF ℓ-REGULAR PARTITION FUNCTIONS

DOI10.1142/S1793042108001341zbMath1221.11208MaRDI QIDQ3602978

David Penniston

Publication date: 12 February 2009

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

zbMATH Keywords

Partitionsmodular forms

Mathematics Subject Classification ID

Partitions; congruences and congruential restrictions (11P83) Holomorphic modular forms of integral weight (11F11)

Related Items (38)

Parity results for 7-regular and 23-regular partitions ⋮ Congruences for (3,11)-regular bipartitions modulo 11 ⋮ An infinite family of congruences modulo 3 for 13-regular bipartitions ⋮ GENERALISATION OF KEITH’S CONJECTURE ON 9-REGULAR PARTITIONS AND 3-CORES ⋮ Congruences for 7 and 49-regular partitions modulo powers of 7 ⋮ New congruences for \(\ell\)-regular overpartition pairs ⋮ Congruences of \(\ell\)-regular partition triples for \(\ell\in\{2, 3, 4, 5\}\) ⋮ Congruences for some \(l\)-regular partitions modulo \(l\) ⋮ Arithmetic properties of partitions with even parts distinct ⋮ -REGULAR PARTITIONS AND MODULAR FORMS WITH COMPLEX MULTIPLICATION ⋮ Certain Diophantine equations and new parity results for 21-regular partitions ⋮ 4-regular partitions and the pod function ⋮ 6-regular partitions: new combinatorial properties, congruences, and linear inequalities ⋮ Congruences modulo \(4\) for the number of \(3\)-regular partitions ⋮ Congruences modulo powers of 5 for two restricted bipartitions ⋮ Parity results for 13-regular partitions and broken 6-diamond partitions ⋮ On \(\ell \)-regular bipartitions modulo \(\ell \) ⋮ Arithmetic properties for 7-regular partition triples ⋮ Arithmetic Properties For $(r,s)$-Regular Partition Functions With Distinct Parts ⋮ Congruences for \(\ell\)-regular overpartition for \(\ell \in \{5,6,8\}\) ⋮ Congruences modulo 9 for singular overpartitions ⋮ Unnamed Item ⋮ Parity results for 9-regular partitions ⋮ New infinite families of congruences modulo 8 for partitions with even parts distinct ⋮ Congruences for \(\ell\)-regular partition functions modulo 3 ⋮ Arithmetic properties of $\ell$-regular overpartition pairs ⋮ Arithmetic of the 7-regular bipartition function modulo 3 ⋮ Congruences for 5-regular partitions modulo powers of 5 ⋮ A PROOF OF KEITH'S CONJECTURE FOR 9-REGULAR PARTITIONS MODULO 3 ⋮ Arithmetic properties of 7-regular partitions ⋮ Arithmetic of the 13-regular partition function modulo 3 ⋮ Arithmetic properties of l-regular overpartitions ⋮ THE 7-REGULAR AND 13-REGULAR PARTITION FUNCTIONS MODULO 3 ⋮ 11-Regular partitions and a Hecke eigenform ⋮ Arithmetic properties for \(\ell\)-regular partition functions with distinct even parts ⋮ Some new congruences for \((j, k)\)-regular bipartition triples ⋮ ARITHMETIC PROPERTIES OF -REGULAR BIPARTITIONS ⋮ On 3-divisibility of 9- and 27-regular partitions

Cites Work

• Divisibility of certain partition functions by powers of primes
• Distribution of the partition function modulo composite integers \(M\)
• Distribution of the partition function modulo \(m\)
• The arithmetic of partitions into distinct parts
• Congruence properties for the partition function
• CONGRUENCES FOR THE COEFFICIENTS OF WEAKLY HOLOMORPHIC MODULAR FORMS
• Divisibility and distribution of partitions into distinct parts

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