On flat polynomials with non-Negative coefficients

TL;DR

This paper establishes a necessary condition for sequences of non-negative coefficient trigonometric polynomials to be flat almost everywhere, advancing understanding of their structural properties.

Contribution

It introduces a new necessary condition for flatness in non-negative coefficient polynomials, providing theoretical insight into their behavior.

Findings

Identifies a key necessary condition for flatness

Advances theoretical understanding of flat polynomials

Provides groundwork for further research in polynomial flatness

Abstract

We formulate and prove a necessary condition for a sequence of analytic trigonometric polynomials with real non-negative coefficients to be flat a.e.