New congruences modulo 4 and 8 for Ramanujan's \(\phi\) function

DOI10.1090/PROC/17109MaRDI QIDQ6668369

Jeremy Lovejoy, Olivia X. M. Yao, Julia Q. D. Du

Publication date: 22 January 2025

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

mock theta functionscongruencesNewman's identitiesRamanujan's \(\phi\) function

Mathematics Subject Classification ID

Combinatorial aspects of partitions of integers (05A17) Partitions; congruences and congruential restrictions (11P83) Elementary theory of partitions (11P81)

Cites Work

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• Umbral moonshine
• Explicit congruences modulo 2048 for overpartitions
• A proof of the mod 4 unimodal sequence conjectures and related mock theta functions
• Arithmetic properties of Schur-type overpartitions
• Proofs of some conjectures of Chan on Appell-Lerch sums
• Automorphic properties of generating functions for generalized odd rank moments and odd Durfee symbols
• Identities for Ramanujan's Sixth-Order Mock Theta Functions
• Congruences for Ramanujan's φ function
• Further Identities and Congruences for the Coefficients of Modular Forms
• Periodicity Modulo m and Divisibility Properties of the Partition Function
• CONGRUENCES MODULO 4 FOR WEIGHT ETA-PRODUCTS
• New congruence properties for Ramanujan’s 𝜙 function
• On Ramanujan's lost notebook and new tenth‐order like identities for second‐, sixth‐, and eighth‐order mock theta functions
• Congruences modulo powers of 5 for Ramanujan's \(\phi\) function

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