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

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• 作者：Chadwick Gugg ^{cgugg@canes.gsw.edu}
• 关键词：primary ; 11A55 ; 33D90 ; secondary ; 11P83
• 刊名：Journal of Number Theory
• 出版年：2012
• 期刊代码：78_0022314x
• 类别：mt
• 出版时间：July, 2012
• 卷：132
• 期：7
• 页码：1519-1553
• 文件大小：312 K

摘要

In this paper, we prove modular identities involving cubes of the Rogers-Ramanujan functions. Applications are given to proving relations for the Rogers-Ramanujan continued fraction. Some of our identities are new. We establish analogous results for the Ramanujan-G枚llnitz-Gordon functions and the Ramanujan-G枚llnitz-Gordon continued fraction. Finally, we offer applications to the theory of partitions.