Vertex operator algebras and the zeta function

1999/09/29 by James Lepowsky, Lepowsky, James
Mathematics · Physics and Astronomy · #17B65 #17B66 #17B68 #17B69 (Primary) 11M06 #81T40 (Secondary) #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Nonlinear Waves and Solitons #Number Theory (math.NT) #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Rings and Algebras (math.RA) #hep-th #math.NT #math.QA #math.RA #math.RT #msc:11M06 #msc:17B65 #msc:17B66 #msc:17B68 #msc:17B69 #msc:81T40

paper · pdf · doi:10.48550/arxiv.math/9909178

21 pages, LaTeX, to be published in Contemporary Math., Vol. 248

arxiv created 1999/09/29 · openalex publication_date 1999/09/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We announce a new type of "Jacobi identity" for vertex operator algebras, incorporating values of the Riemann zeta function at negative integers. Using this we "explain" and generalize some recent work of S. Bloch's relating values of the zeta function with the commutators of certain operators and Lie algebras of differential operators.

Citations

• Local systems of vertex operators, vertex superalgebras and modules

Related

• Application of a "Jacobi identity" for vertex operator algebras to zeta values and differential operators
• Formal differential operators, vertex operator algebras and zeta--values, I
• Introduction to vertex operator algebras II
• A classical vertex algebra constructed with the use of some logarithmic formal calculus
• Formal differential operators, vertex operator algebras and zeta--values , II