Ramanujan-Type Series of Signature 2: Analytical Evaluation via Degree-2 Modular Transformations

Pablo Fernández Refolio

Ramanujan-Type Series of Signature 2: Analytical Evaluation via Degree-2 Modular Transformations

General Mathematics 2026-07-26 v1

Authors: Pablo Fernández Refolio

Abstract

We provide an explicit analytical evaluation of Ramanujan-type series for $1/\pi$ 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.

Keywords

ramanujan-type series signature 2 singular moduli modular transformations elliptic identities analytical evaluation

Cite

@article{arxiv.2607.24867,
  title  = {Ramanujan-Type Series of Signature 2: Analytical Evaluation via Degree-2 Modular Transformations},
  author = {Pablo Fernández Refolio},
  journal= {arXiv preprint arXiv:2607.24867},
  year   = {2026}
}

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11 Pages