The Möbius pseudodistance of the annulus and an improved lower bound for Korenblum's constant

We show that Korenblum's constant of the Bergman space satisfies $c_2\ge 0.446$. The best published lower bound was $c_2\ge 0.4263$ (Wikström, 2026). The new ingredient is a closed form, in Jacobi theta functions, of the Möbius pseudodistance of the annulus $\{c<|z|<1\}$ between two points of the same centred circle. It separates the variables and yields three monotonicity properties, one of which, a profile inequality, combined with Kirszbraun's theorem in the hyperbolic plane, improves the constant in Wang's annular estimate. Wikström's dual moment criterion is then verified at $c=223/500$ for an explicit measure with fourteen rational atoms, in rigorous arithmetic, by a self-contained verifier. The French version of this note is dated 21 October 2026.