PreprintarXiv licencearXiv
Ramanujan-Type Series of Signature 2: Analytical Evaluation via Degree-2 Transformations and Associated Harmonic Expansions
Abstract
We provide an explicit analytical evaluation of the known rational Ramanujan-type series for the theory of signature 2. Focusing on the singular moduli kr for r ∈ {2, 3, 4, 7}, we demonstrate that the underlying elliptic identities can be established through modular transformations of degree 2. In particular, we showcase a family of rational harmonic Ramanujan-type series for 1/π involving higher-degree polynomials
Related
- Analytical Evaluation of Ramanujan Series for 1/π via Degree-2, Degree-3, Degree-7, and Degree-19 Modular Transformations
- A Four-Genus Kronecker-Limit Evaluation of the Alternating Rogers-Ramanujan Continued Fraction
- Ramanujan Challenge Results: AI-Assisted Evaluation Pipeline for Multi-Format Proofs
- Eta-Quotient Representations for a Three Parameter Family of Modular Functions Associated with the Rogers-Ramanujan Continued Fraction
- Littlewood-Paley theory for orthogonal expansions associated with root systems
BibTeX
@misc{refolio2026ramanujantype,
title = {{Ramanujan-Type Series of Signature 2: Analytical Evaluation via Degree-2 Transformations and Associated Harmonic Expansions}},
author = {Pablo Fernández Refolio},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.24867},
eprint = {2607.24867},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.24867},
}
RIS
TY - UNPB
TI - Ramanujan-Type Series of Signature 2: Analytical Evaluation via Degree-2 Transformations and Associated Harmonic Expansions
AU - Pablo Fernández Refolio
PY - 2026
DA - 2026/09/26
PB - arXiv
DO - 10.48550/arxiv.2607.24867
UR - https://arxiv.org/abs/2607.24867
AB - We provide an explicit analytical evaluation of the known rational Ramanujan-type series for the theory of signature 2. Focusing on the singular moduli k_r for r ∈ {2, 3, 4, 7}, we demonstrate that the underlying elliptic identities can be established through modular transformations of degree 2. In particular, we showcase a family of rational harmonic Ramanujan-type series for 1/π involving higher-degree polynomials
ER -