On a conjecture for higher-order Szego theorems

TL;DR

This paper disproves a longstanding conjecture related to higher-order Szego theorems for orthogonal polynomials on the unit circle and offers a revised conjecture to better fit the observed mathematical phenomena.

Contribution

The authors disprove Simon's conjecture for higher-order Szego theorems and introduce a modified conjecture to advance understanding in the field.

Findings

Disproved Simon's conjecture for higher-order Szego theorems

Proposed a revised conjecture consistent with new findings

Enhanced theoretical understanding of orthogonal polynomials on the unit circle

Abstract

We disprove a conjecture of Simon for higher-order Szego theorems for orthogonal polynomials on the unit circle and propose a modified version of the conjecture.