Landau’s constant

We suggest that the reader reads first the entry on Bloch’s constant. Let be the set of all functions f holomorphic on a region containing the closure of the disk D={z:|z|<1} and satisfying f(0)=0 and f(0)=1. For each f let λ(f) be the supremum of all numbers r such that there is a disk SD such that f(S) contains a disk of radius r (notice that here we don’t require f to be injectivePlanetmathPlanetmath on S).


Landau’s constant L is defined by


Let B be Bloch’s constant. Then, clearly, LB. The exact value of L (as that of B) is not known but it has been shown that 0.5L0.56. In particular, it is known that L is strictly greater than B.


  • 1 John B. Conway, Functions of One Complex Variable I, Second Edition, 1978, Springer-Verlag, New York.
Title Landau’s constant
Canonical name LandausConstant
Date of creation 2013-03-22 15:58:07
Last modified on 2013-03-22 15:58:07
Owner alozano (2414)
Last modified by alozano (2414)
Numerical id 4
Author alozano (2414)
Entry type Definition
Classification msc 32H02
Related topic BlochsConstant