2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/166494Let 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).18 pagesClassical Analysis and ODEsComplex Variables30C10text