We gratefully acknowledge support from
the Simons Foundation and member institutions.
Full-text links:

Download:

Current browse context:

math.CV
< prev | next >
new | recent | 0805

Change to browse by:

math

References & Citations

Bookmark

(what is this?)
CiteULike logo BibSonomy logo Mendeley logo del.icio.us logo Digg logo Reddit logo

Mathematics > Complex Variables

Title: On the length of lemniscates

Authors: Alexandre Eremenko, Walter Hayman
(Submitted on 15 May 2008 (v1), last revised 27 Mar 2024 (this version, v2))
Abstract: We show that for a monic polynomial p of degree d, the length of the level set {z: |p(z)|=1} is at most 9.2 d, which improves an earlier estimate due to P. Borwein. For d=2 we show that the extremal level set is the Bernoullis' Lemniscate. One ingredient of our proofs is the fact that for an extremal polynomial this level set is connected.
Subjects: Complex Variables (math.CV)
MSC classes: 30C10
Journal reference: Michigan Math. J., 46 (1999), 409-415
Cite as: arXiv:0805.2295 [math.CV]
  (or arXiv:0805.2295v2 [math.CV] for this version)

Submission history

From: Alexandre Eremenko [view email]
[v1] Thu, 15 May 2008 13:11:33 GMT (8kb)
[v2] Wed, 27 Mar 2024 12:18:40 GMT (8kb)
Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)

Link back to: arXiv, form interface, contact.