Author

Frank Wikström

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Preprint Oct 2026

A computer-assisted proof of Krzy\.z's conjecture for the sixth coefficient

We prove Krzy\.z's conjecture for the sixth coefficient. Every holomorphic function $f(z)=\sum a_kz^k$ from the unit disk to the punctured disk satisfies $|a_6| \le 2/e$. Equality holds precisely for rotations of $\exp(-(1-z^6)/(1+z^6))$. Every extremal has a Herglotz representation with at most six atoms. By the reduc...

Frank Wikström · 0 citations

Preprint Sep 2026

A computer-assisted lower bound for Landau's constant

We prove the lower bounds \[ B_\infty>0.51,\qquad L>0.51, \] where $B_\infty$ is the locally univalent Bloch constant and $L$ is Landau's constant, improving the bound $\frac{1}{2}+2\cdot10^{-8}$ of Chen and Shiba. The argument passes to the logarithm $g=\log f'$ of a normalized locally univalent Bloch function, where...

Frank Wikström · 0 citations

Preprint Aug 2026

An improved lower bound for Bloch's constant

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 ($\sqrt{3}/4+2\cdot10^{-4}$) and Xiong ($\sqrt{3}/4+3\cdot10^{-4}$). The proof refines Bonk's method through computer-assisted estimates rigorously verified using interval ar...

Frank Wikström · 0 citations