Top Qs
Timeline
Chat
Perspective
Polya's shire theorem
Theorem in complex analysis From Wikipedia, the free encyclopedia
Remove ads
Pólya's shire theorem, named after George Pólya, is a theorem in complex analysis that describes the asymptotic distribution of the zeros of successive derivatives of a meromorphic function on the complex plane.[1] It has applications in Nevanlinna theory.[2]: 55, 62
Statement
Summarize
Perspective
Let be a meromorphic function on the complex plane with as its set of poles. If is the set of all zeros of all the successive derivatives , then the derived set (or the set of all limit points) is as follows:
- if has only one pole, then is empty.
- if , then coincides with the edges of the Voronoi diagram determined by the set of poles . In this case, if , the interior of each Voronoi cell consisting of the points closest to than any other point in is called the -shire.[3]
The derived set is independent of the order of each pole.[3]: 32
Remove ads
References
Further reading
Wikiwand - on
Seamless Wikipedia browsing. On steroids.
Remove ads