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

Tamás Erdélyi

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

Classical Analysis and ODEs 2026-08-01 v1

Authors: Tamás Erdélyi

Abstract

Making a progress in an Erd\"os problem dating back to 1957, we show that $\max_{t \in {\Bbb R}}{|P_n(e^{it})|^2} \geq n+1 + \frac{1}{38}n^{1/3}$ for every polynomial $P_n$ of degree $n$ with all of its coefficients in $\{-1,1\}$ .

Keywords

Littlewood polynomial maximum modulus unit circle Erdos problem trigonometric polynomial

Cite

@article{arxiv.2608.00744,
  title  = {On an Erdös Problem about the Maximum Modulus of Littlewood Polynomials on the Unit Circl},
  author = {Tamás Erdélyi},
  journal= {arXiv preprint arXiv:2608.00744},
  year   = {2026}
}