Linear independence measures for Chowla--Selberg periods

Wadim Zudilin

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arXiv · 2508.17738

Linear independence measures for Chowla--Selberg periods

Wadim Zudilin

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Abstract

We use simultaneous Pad\'e approximations to $_3F_2$ hypergeometric functions to estimate from below linear forms in $1$, $\pi\sqrt d$, $\Omega_D/\pi$ and $\pi/\Omega_D$ with integral coefficients, for certain choices of positive integer $d$ and negative integer $D$, where $\Omega_D$ is (the square of) a Chowla--Selberg period attached to the imaginary quadratic field $Q(\sqrt{D})$.

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Wadim Zudilin. 2025-08-25. Linear independence measures for Chowla--Selberg periods. https://arxiv.org/abs/2508.17738

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