A lower bound for the Bohr radius of the bidisc

We prove that the Bohr radius K₂ of the bidisc, whose exact value is unknown, satisfies K₂ > 0.301665, improving Patel's bound K₂ > 0.30158758. As in his argument, we pass to functions with positive real part and value 1 at the origin; we bound the sum of the moduli of their coefficients of degree n by 2S_n instead of 2√n, where S_n is the Sidon constant of {0, 1, …, n}, and we bound S₅, S₆ and S₇ with computer-assisted certificates. In Lean 4 we also prove K₂ ≥ 0.301665, assuming Patel's inequality coupling the coefficients of degrees two and three.

This version revises the presentation; the results are unchanged from version 5. The certificates, programs and Lean files are archived at doi:10.5281/zenodo.23716440, and everything except the largest certificate files and an archive of generated Lean modules is also at github.com/tejasvi/bidisc-bohr-radius/tree/v6.