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

JOURNAL OF NUMBER THEORY

卷:132

Article

Gugg, Chadwick

关键词: Rogers-Ramanujan functions;    Rogers-Ramanujan continued fraction;    Ramanujan-Gollnitz-Gordon functions;    Ramanujan-Gollnitz-Gordon continued fraction;    Ramanujan's notebooks;    Modular identities;    Theta functions;    Partitions;    Colored partitions;   

DOI  :  10.1016/j.jnt.2012.01.005

来源: Elsevier

【 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-Gollnitz-Gordon functions and the Ramanujan-Gollnitz-Gordon continued fraction. Finally, we offer applications to the theory of partitions. (C) 2012 Elsevier Inc. All rights reserved,

【 授权许可】

Free