Ramanujan-Type Series of Signature 2: Analytical Evaluation via Degree-2 Transformations and Associated Harmonic Expansions
Year: 2026
Type: preprint
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 $k_r$ for $r \in \{2, 3, 4, 7\}$, 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
Source: arXiv (Cornell University)
Author: Refolio, Pablo Fernández
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7171617094