New estimates for the length of the Erdos-Herzog-Piranian lemniscate

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dc.creatorFryntov, Alexander
dc.creatorNazarov, Fedor
dc.date2008-08-05
dc.date.accessioned2026-07-07T09:54:55Z
dc.date.available2026-07-07T09:54:55Z
dc.descriptionLet p(z) be a monic polynomial of degree n. Consider the lemniscate L={z:|p(z)|=1}. It has been conjectured that L has the largest length when p(z)=z^n-1. We show that the length of L attains a local maximum at this polynomial and prove the asymptotically sharp bound |L|<2n+o(n).
dc.description18 pages
dc.identifierhttps://arxiv.org/abs/0808.0717
dc.identifierhttp://arxiv.org/abs/0808.0717
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/166494
dc.subjectClassical Analysis and ODEs
dc.subjectComplex Variables
dc.subject30C10
dc.titleNew estimates for the length of the Erdos-Herzog-Piranian lemniscate
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