An Explicit Cubic Ramanujan--Sato Series for $1/π$ on $Γ_0(2)^+$ at $D=-163$

Vedran Menđušić

An Explicit Cubic Ramanujan--Sato Series for $1/π$ on $Γ_0(2)^+$ at $D=-163$

Number Theory 2026-06-27 v1

Authors: Vedran Menđušić

Abstract

An explicit cubic Ramanujan--Sato formula for $1/\pi$ on $\Gamma_0(2)^+$ at $D=-163$ is presented. The construction produces a very small cubic CM parameter, giving about $15.01$ decimal digits of geometric contraction per term. This is slightly sharper than the classical Chudnovsky contraction, but the coefficients lie in a cubic algebraic field.

Keywords

Ramanujan-Sato series 1/pi modular forms CM parameters Gamma_0(2)^+

Cite

@article{arxiv.2606.28966,
  title  = {An Explicit Cubic Ramanujan--Sato Series for $1/π$ on $Γ_0(2)^+$ at $D=-163$},
  author = {Vedran Menđušić},
  journal= {arXiv preprint arXiv:2606.28966},
  year   = {2026}
}

Comments

10 pages; ancillary verification scripts included