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Certain Somos’s \(\varvec{P}\)\(\varvec{Q}\) type Dedekind \(\varvec{\eta }\)-function identities

  • B R Srivatsa Kumar
  • H C Vidya
Article
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Abstract

In this paper, we provide a new proof for the Dedekind \(\eta \)-function identities discovered by Somos. During this process, we found two new Dedekind \(\eta \)-function identities. Furthermore, we extract interesting partition identities from some of the \(\eta \)-function identities.

Keywords

Dedekind \(\eta \)-function theta functions modular equations colored partitions 

2010 Mathematics Subject Classification

Primary: 11F20 11B65 11P83 Secondary: 14K25 

Notes

Acknowledgements

The authors are extremely grateful to the referee for numerous suggestions which have significantly improved the presentation of this work. The authors would also like to thank Dr. K R Vasuki, Department of Studies in Mathematics, Manasa Gangothri, University of Mysore, Mysore, India for his guidance during the preparation of this paper. The research of the first author is partially supported under Extra Mural Research Funding by SERB, a statutory body of DST, Government of India (File No. EMR/2016/001601).

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Copyright information

© Indian Academy of Sciences 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Manipal Institute of TechnologyManipal Academy of Higher EducationManipalIndia

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