Application of a "Jacobi identity" for vertex operator algebras to zeta values and differential operators

1999/09/30 by James Lepowsky
Mathematics · Physics and Astronomy · #math.QA #hep-th #math.NT #math.RA #math.RT #msc:17B69 #msc:11M06 #msc:17B65 #msc:17B66 #msc:17B68 #msc:81T40

paper · pdf

published as Lett.Math.Phys. 53 (2000) 87-103 · 20 pages, LaTeX; more exposition and two references added; to appear in Letters in Mathematical Physics

arxiv created 2000/10/17 · arxiv updated 2009/11/30

Abstract

We explain how to use a certain new "Jacobi identity" for vertex operator algebras, announced in a previous paper (math.QA/9909178), to interpret and generalize recent work of S. Bloch's relating values of the Riemann zeta function at negative integers with a certain Lie algebra of operators.

Related

• Vertex operator algebras and the zeta function
• Formal differential operators, vertex operator algebras and zeta--values, I
• A classical vertex algebra constructed with the use of some logarithmic formal calculus
• Formal differential operators, vertex operator algebras and zeta--values , II
• Linear automorphisms of vertex operator algebras associated with formal changes of variable and Bernoulli-type numbers