Modular equations for cubes of the Rogers-Ramanujan and Ramanujan-Göllnitz-Gordon functions and their associated continued fractions

DOI10.1016/j.jnt.2012.01.005zbMath1271.11020OpenAlexW2058114043MaRDI QIDQ415257

Chadwick Gugg

Publication date: 11 May 2012

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

Full work available at URL: https://doi.org/10.1016/j.jnt.2012.01.005

zbMATH Keywords

partitionstheta functionscolored partitionsRogers-Ramanujan functionsRogers-Ramanujan continued fractionmodular identitiesRamanujan-Göllnitz-Gordon continued fractionRamanujan-Göllnitz-Gordon functionsRamanujan's notebooks

Mathematics Subject Classification ID

Binomial coefficients; factorials; (q)-identities (11B65) Partitions; congruences and congruential restrictions (11P83) Theta series; Weil representation; theta correspondences (11F27) Continued fractions (11A55) Applications of basic hypergeometric functions (33D90)

Related Items (5)

New modular relations involving cubes of the Göllnitz-Gordon functions ⋮ Modular relations for the Rogers-Ramanujan functions with applications to partitions ⋮ New congruences modulo 5 for the number of 2-color partitions ⋮ A new proof of Ramanujan's modular equation relating \(R(q)\) with \(R(q^{5})\) ⋮ THE ROGERS–RAMANUJAN CONTINUED FRACTION AND RELATED ETA-QUOTIENT REPRESENTATIONS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Elementary proofs of some identities of Ramanujan for the Rogers-Ramanujan functions
• Two modular equations for squares of the Rogers-Ramanujan functions with applications
• Arithmetic of the Ramanujan-Göllnitz-Gordon continued fraction
• A generalization of a modular identity of Rogers
• A new proof of Ramanujan's modular equation relating \(R(q)\) with \(R(q^{5})\)
• On the Ramanujan-Göllnitz-Gordon continued fraction
• On modular relations for the Göllnitz-Gordon functions with application to partitions
• Modular equations for the Rogers-Ramanujan continued fraction and the Dedekind eta-function
• New modular relations for the Göllnitz-Gordon functions.
• Some new proofs of modular relations for the Göllnitz-Gordon functions
• Some continued fractions of the Rogers-Ramanujan type
• Certain identities for Ramanujan-Göllnitz-Gordon continued fraction
• A Fundamental Modular Identity and Some Applications
• COMMON SOURCE OF NUMEROUS THETA FUNCTION IDENTITIES
• A Proof of some identities of Ramanujan using modular forms
• A look back at Ramanujan's Notebooks
• Some Identities Involving Rogers-Ramanujan-Type Functions
• Some theta function identities related to the Rogers-Ramanujan continued fraction
• ON q-DIFFERENCE EQUATIONS FOR CERTAIN WELL-POISED BASIC HYPERGEOMETRIC SERIES
• Partitionen mit Differenzenbedingungen.
• Ramanujan’s forty identities for the Rogers-Ramanujan functions
• Further Identities of the Rogers-Ramanujan Type

This page was built for publication: Modular equations for cubes of the Rogers-Ramanujan and Ramanujan-Göllnitz-Gordon functions and their associated continued fractions