We suggest that the reader reads first the entry on Bloch’s constant. Let be the set of all functions holomorphic on a region containing the closure of the disk and satisfying and . For each let be the supremum of all numbers such that there is a disk such that contains a disk of radius (notice that here we don’t require to be injective on ).
Landau’s constant is defined by
Let be Bloch’s constant. Then, clearly, . The exact value of (as that of ) is not known but it has been shown that . In particular, it is known that is strictly greater than .
- 1 John B. Conway, Functions of One Complex Variable I, Second Edition, 1978, Springer-Verlag, New York.
|Date of creation||2013-03-22 15:58:07|
|Last modified on||2013-03-22 15:58:07|
|Last modified by||alozano (2414)|