Linear independence measures for Chowla--Selberg periods

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