Bloch’s constant
Bloch’s theorem can be stated in the following way:
Bloch’s Theorem.
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
on which is injective and contains a disk
of radius . Let be the infimum of all , for . Then .
The constant is usually referred to as Bloch’s constant. Nowadays, better bounds are known and, in fact, it has been conjectured that has the following tantalizing form
where is the gamma function.
References
- 1 John B. Conway, Functions of One Complex Variable I, Second Edition, 1978, Springer-Verlag, New York.
Title | Bloch’s constant |
---|---|
Canonical name | BlochsConstant |
Date of creation | 2013-03-22 15:58:04 |
Last modified on | 2013-03-22 15:58:04 |
Owner | alozano (2414) |
Last modified by | alozano (2414) |
Numerical id | 5 |
Author | alozano (2414) |
Entry type | Definition |
Classification | msc 32H02 |
Related topic | LandausConstant |