PreprintCC BY 4.0arXiv
Eta-Quotient Representations for a Three Parameter Family of Modular Functions Associated with the Rogers-Ramanujan Continued Fraction
Abstract
In 2021, Chern and Tang introduced two families of two-parameter modular functions associated with the Rogers-Ramanujan continued fraction. They established recurrence relations that express the members of these families in terms of eta quotients, and used these expressions to obtain dissection formulas. Motivated by their work, we construct a three-parameter extension and derive the corresponding recursive eta quotient representations. Our result also has applications to dissection formulas. In particular, it is used in separate work to obtain $5$-dissection formulas for overpartitions with restricted odd differences.
Related
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- On Ramanujan's cubic continued fraction, II
- A Four-Genus Kronecker-Limit Evaluation of the Alternating Rogers-Ramanujan Continued Fraction
- Logarithmic moments of the Rogers-Ramanujan continued fraction and odd zeta values
- A Ramanujan Pell K3 Surface and Cube Representations
BibTeX
@misc{paudel2026etaquotient,
title = {{Eta-Quotient Representations for a Three Parameter Family of Modular Functions Associated with the Rogers-Ramanujan Continued Fraction}},
author = {Bishnu Paudel and James A. Sellers and Haiyang Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.13131},
eprint = {2609.13131},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.13131},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Eta-Quotient Representations for a Three Parameter Family of Modular Functions Associated with the Rogers-Ramanujan Continued Fraction
AU - Bishnu Paudel
AU - James A. Sellers
AU - Haiyang Wang
PY - 2026
DA - 2026/09/11
PB - arXiv
DO - 10.48550/arxiv.2609.13131
UR - https://arxiv.org/abs/2609.13131
AB - In 2021, Chern and Tang introduced two families of two-parameter modular functions associated with the Rogers-Ramanujan continued fraction. They established recurrence relations that express the members of these families in terms of eta quotients, and used these expressions to obtain dissection formulas. Motivated by their work, we construct a three-parameter extension and derive the corresponding recursive eta quotient representations. Our result also has applications to dissection formulas. In particular, it is used in separate work to obtain $5$-dissection formulas for overpartitions with restricted odd differences.
ER -