An Explicit Cubic Ramanujan--Sato Series for $1/\pi$ on $\Gamma_0(2)^+$ at $D=-163$

Vedran Menđušić

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arXiv · 2606.28966

An Explicit Cubic Ramanujan--Sato Series for $1/\pi$ on $\Gamma_0(2)^+$ at $D=-163$

Vedran Menđušić

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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.

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Vedran Menđušić. 2026-06-27. An Explicit Cubic Ramanujan--Sato Series for $1/\pi$ on $\Gamma_0(2)^+$ at $D=-163$. https://arxiv.org/abs/2606.28966

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