Formal differential operators, vertex operator algebras and zeta--values, I

Details Formal differential operators, vertex operator algebras and zeta--values, I Formal differential operators, vertex operator algebras and zeta--values, I

2003-03-12

arxiv.org/abs/math/0303152v1

Mathematics

Quantum Algebra

52 pages, LaTeX (10pt, small font), BibTex

Scientific paper

We study relationships between spinor representations of certain Lie algebras and Lie superalgebras of differential operators on the circle and values of $\zeta$--functions at the negative integers. By using formal calculus techniques we discuss the appearance of values of $\zeta$--functions at the negative integers underlying the construction. In addition we provide a conceptual explanation of this phenomena through several different notions of normal ordering via vertex operator algebra theory. We also derive a general Jacobi--type identity generalizing our previous construction. At the end we discuss related constructions associated to Dirichlet $L$--functions.

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