Pablo Fernández Refolio

arXiv2026

Ramanujan-Type Series of Signature 2: Analytical Evaluation via Degree-2 Transformations and Associated Harmonic Expansions

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

math.GM↗

arXiv2026

Analytical Evaluation of Ramanujan Series for $1/π$ via Degree-2, Degree-3, Degree-7, and Degree-19 Modular Transformations

We provide an explicit analytical evaluation of Ramanujan-type series for $1/π$. Focusing on the singular moduli $k_{r}$ for $r \in \{5, 7, 13, 37\}$, we demonstrate that the underlying elliptic identities can be established through lower-degree modular transformations. Specifically, we resolve the case $r = 5$ via a combination of degree-2 and degree-3 modular transformations; the case $r = 7$ utilizing the modular transformation of degree 2; the case $r = 13$ via a combination of degree-2 and degree-7 modular transformations; and the case $r = 37$ via a combination of degree-2 and degree-19 modular transformations.

math.GM↗