Arithmetic properties for a partition function related to the Ramanujan/Watson mock theta function \(\omega (q)\)

DOI10.1007/s11139-018-0004-0zbMath1422.11215OpenAlexW2800770296MaRDI QIDQ721852

Ernest X. W. Xia

Publication date: 20 July 2018

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11139-018-0004-0

zbMATH Keywords

partitionsmock theta functionscongruencestheta function identities

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)

Related Items (7)

A polynomial method for proving congruences of pω(n,m) and pν(n,m) ⋮ Congruences for the coefficients of a pair of third and sixth order mock theta functions ⋮ Parity of coefficients of mock theta functions ⋮ Proofs of Silva-Sellers' conjectures on a mock theta function ⋮ New congruences modulo 5 for partition related to mock theta function \(\omega (q)\) ⋮ Generating functions and congruences for some partition functions related to mock theta functions ⋮ Identities, inequalities and congruences for odd ranks and \(k\)-marked odd Durfee symbols

Cites Work

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• More infinite families of congruences modulo 5 for broken 2-diamond partitions
• New congruences for partitions related to mock theta functions
• Identities and congruences for Ramanujan's \(\omega (q)\)
• Partitions associated with the Ramanujan/Watson mock theta functions \(\omega(q)\), \(\nu(q)\) and \(\phi(q)\)
• \(p\)-adic properties of Maass forms arising from theta series
• Congruences related to the Ramanujan/Watson mock theta functions \(\omega (q)\) and \(\nu (q)\)
• Congruences modulo 16, 32, and 64 for Andrews's singular overpartitions
• On certain explicit congruences for mock theta functions
• Ramanujan’s “Most Beautiful Identity”
• The Final Problem : An Account of the Mock Theta Functions

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