Vedran Menđušić | Searcharxiv

arXiv2026

Class-Number-One Cubic Fricke Companions on $Γ_0(2)^+$ and an Exact Chudnovsky Bridge

A structural classification-and-bridge result is proved for RS series on $Γ_0(2)^+$. Among the fundamental Heegner discriminants with $h(D)=1$, the irreducibly cubic Fricke-cusp companions occur exactly for \[ D=-11,-19,-43,-67,-163. \] The proof gives an explicit bridge between $z=1728/j$ and $X=256t/(t+64)^2$, a hypergeometric gauge identity, and a CM interpretation of the fibre. For $D=-163$, the cubic Fricke RS series is the exact level-two transport of the Chudnovsky linear form.

math.NT↗

arXiv2026

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

An explicit cubic Ramanujan--Sato formula for $1/π$ on $Γ_0(2)^+$ 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.

math.NT↗