Character formulas in terms of R_β and R_m functions

M. P. Chaudhary, Sangeeta Chaudhary and Kamel Mazhouda
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 28, 2022, Number 1, Pages 1–8
DOI: 10.7546/nntdm.2022.28.1.1-8
Full paper (PDF, 225 Kb)

Details

Authors and affiliations

M. P. Chaudhary
Department of Mathematics, Netaji Subhas University of Technology
Sector 3, Dwarka, New Delhi 110078, India

Sangeeta Chaudhary
School of Computer & System Sciences, Jawaharlal Nehru University
New Delhi 110067, India

Kamel Mazhouda
Department of Mathematics, University of Monastir
Monastir 5000, Tunisia

Abstract

The authors establish a set of fourteen character formulas in terms of R_β and R_m functions. Folsom [6] studied character formulas and Chaudhary [5] expressed those formulas in terms of continued fraction identities. Andrews et al. [2] introduced multivariate R-functions, which are further classified as R_α; R_β, and R_m (for m = 1, 2, 3, …) functions by Srivastava et al. [10].

Keywords

• q-product identities
• Character formulas
• R_α, R_β and R_m functions

2020 Mathematics Subject Classification

• 05A30
• 11F27
• 05A17
• 11P83

References

1. Andrews, G. E. (1998). The Theory of Partitions, Cambridge University Press, Cambridge.
2. Andrews, G. E., Bringman K., & Mahlburg, K. (2015). Double series representations for Schur’s partition function and related identities, Journal of Combinatorial Theory, Series A, 132, 102–119.
3. Apostol, T. M. (1976). Introduction to Analytic Number Theory, Undergraduate Texts in Mathematics, Springer-Verlag New York.
4. Berndt, B. C. (1991). Ramanujan’s Notebooks, Part III, Springer-Verlag New York.
5. Chaudhary, M. P. (2014). Generalization for character formulas in terms of continued fraction identities. Malaya Journal of Matematik, 1(1), 24–34.
6. Folsom, A. (2011). Kac–Wakimoto characters and universal mock theta functions. Transactions of the American Mathematical Society, 363, 439–455.
7. Jacobi, C. G. J. (1829). Fundamenta Nova Theoriae Functionum Ellipticarum. Regiomonti, Sumtibus Fratrum Borntrager, Konigsberg, Germany; Reprinted in  Gesammelte Mathematische Werke, 1 (1829), 497–538, American Mathematical Society, Providence, Rhode Island (1969), 97–239.
8. Ramanujan, S. (1957). Notebooks, Vols. 1 and 2, Tata Institute of Fundamental Research, Bombay.
9. Ramanujan, S. (1988). The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi.
10. Srivastava, H. M., Srivastava, R., Chaudhary, M. P., & Uddin, S. (2020). A family of theta function identities based upon combinatorial partition identities and related to Jacobi’s triple-product identity, Mathematics, 8(6), Article ID 918.

Manuscript history

• Received: 23 May 2021
• Revised: 2 November 2021
• Accepted: 15 December 2021
• Online First: 2 February 2022