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

被引：6
作者：
Gugg, Chadwick [1 ]
机构：
[1] Georgia SW State Univ, Dept Math, Americus, GA 31709 USA
来源：
JOURNAL OF NUMBER THEORY | 2012年 / 132卷 / 07期
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; IDENTITIES; PROOFS;
D O I：
10.1016/j.jnt.2012.01.005
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
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,
引用
收藏
页码：1519 / 1553
页数：35
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