On an Erdös Problem about the Maximum Modulus of Littlewood Polynomials on the Unit Circl

2026/08/01 by Tamás Erdélyi
Mathematics · #math.CA #msc:11C08 #msc:41A17

paper · pdf

arxiv created 2026/08/01 · arxiv updated 2026/08/04

Abstract

Making a progress in an Erdös problem dating back to 1957, we show that max_t ∈ \Bbb R|P_n(e^it)|² ≥ n+1 + (1)/(38)n^1/3 for every polynomial P_n of degree n with all of its coefficients in \-1,1\.

Citations

• Flat Littlewood Polynomials Exist
• Arestov's theorems on Bernstein's inequality
• The asymptotic distance between an ultraflat unimodular polynomial and\n its conjugate reciprocal
• Littlewood Polynomials with Small L⁴ Norm