On rational matrix exact covering systems of Zn and its applications to Ramanujan's forty identities

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:446

Article

Cao, Zhu¹  Hu, Yong² 

[1] Kennesaw State Univ, Dept Math, Marietta, GA 30060 USA

[2] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China

关键词: Covering systems;    q-series;    Theta functions;    Rogers-Ramanujan functions;   

DOI  :  10.1016/j.jmaa.2016.08.051

来源: Elsevier

【 摘 要 】

For a nonsingular integer matrix B, the set of cosets of the quotient module ZnP3Zn forms an exact covering system (ECS) of Z(n). In this paper, we use the Smith normal form to obtain another type of matrix ECS with rational entries which we call rational matrix ECS. Using rational matrix ECS of Z(2), we prove eight identities in Ramanujan's list of forty identities for the Rogers-Ramanujan functions, as well as some other identities. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free