DocServer

The Arc Length of the Lemniscate { | p(z) | = 1 }

Borwein, Peter (1993) The Arc Length of the Lemniscate { | p(z) | = 1 }. [Preprint]

[img]
Preview
Postscript
Download (110Kb) | Preview
    [img]
    Preview
    PDF
    Download (116Kb) | Preview

      Abstract

      We show that the length of the set $$\{z \in {\Bbb C}: \left|\Pi^n_{i=1} (z - \alpha_i) \right| = 1\}$$ is at most $8\pi e n$. This gives the correct rate of growth in a long standing open problem of Erd\"os, Herzog and Piranian and improves the previous bound of $74n^2$ due to Pommerenke.

      Item Type: Preprint
      Additional Information: pubdom FALSE
      Uncontrolled Keywords: capacity, arclength, Erdos, lemniscate, polynomial
      Subjects: 31-xx Potential theory > 31Axx Two-dimensional theory
      26-xx Real functions > 26Dxx Inequalities
      Faculty: UNSPECIFIED
      Depositing User: Users 1 not found.
      Date Deposited: 16 Nov 2003
      Last Modified: 21 Apr 2010 11:13
      URI: https://docserver.carma.newcastle.edu.au/id/eprint/66

      Actions (login required)

      View Item