On D. Haegele's approach to the Bessis-Moussa-Villani conjecture

2007/11/05 by Peter S. Landweber, Landweber, Peter S., Eugène R. Speer +1
Mathematics · #15A45 #15A48 #15A90 #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #FOS: Mathematics #Functional Equations Stability Results #Operator Algebras (math.OA) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.0711.0672

openalex publication_date 2007/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The reformulation of the Bessis-Moussa-Villani conjecture given by Lieb and Seiringer asserts that the coefficient of t^r in the polynomial Trace[(A+tB)^p], with A and B positive semidefinite matrices, is nonnegative for all p and r. We propose a natural extension of a method of attack on this problem due to Haegele, and investigate for what values of p and r the method is successful, obtaining a complete determination when either p or r is odd.

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