An improved lower bound for Bloch's constant

Abstract

Let $B$ denote Bloch's constant. We prove \[ B \ge \frac{\sqrt{3}}{4}+0.0153 = 0.448312701\ldots, \] improving the lower bounds by Chen--Gauthier ($\sqrt{3}/4+2\cdot 10^{-4}$) and Xiong ($\sqrt{3}/4+3\cdot 10^{-4}$). The proof refines Bonk's method through computer-assisted estimates rigorously verified using interval arithmetic.

16 pages