Eisenstein series of level 6 and level 10 with their applications to theta function identities of Ramanujan

A. I. Vijaya Shankar
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 28, 2022, Number 3, Pages 581–588
DOI: 10.7546/nntdm.2022.28.3.581-588
Full paper (PDF, 174 Kb)

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Authors and affiliations

A. I. Vijaya Shankar
Department of Studies in Mathematics, University of Mysore
Manasagangotri, Mysuru – 570 006, Karnataka, India

Abstract

S. Ramanujan recorded theta function identities of different levels in the unorganized pages of his second notebook and the lost notebook. In this paper, we prove level 6 and level 10 theta function identities by using Eisenstein series identities.

Keywords

  • Theta functions
  • Eisenstein series

2020 Mathematics Subject Classification

  • 11F20
  • 11M36

References

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Manuscript history

  • Received: 6 May 2022
  • Revised: 19 September 2022
  • Accepted: 21 September 2022
  • Online First: 28 September 2022

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Cite this paper

Vijaya Shankar, A. I. (2022). Eisenstein series of level 6 and level 10 with their applications to theta function identities of Ramanujan. Notes on Number Theory and Discrete Mathematics, 28(3), 581-588, DOI: 10.7546/nntdm.2022.28.3.581-588.

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