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

✍ Scribed by Antun Milas

Publisher: Elsevier Science
Year: 2003
Tongue: English
Weight: 551 KB
Volume: 183
Category: Article
ISSN: 0022-4049
DOI: 10.1016/s0022-4049(03)00035-5

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✦ Synopsis

We study relationships between spinor representations of certain Lie algebras and Lie superalgebras of di erential operators on the circle and values of -functions at the negative integers. By using formal calculus techniques we discuss the appearance of values of -functions at the negative integers underlying the construction. In addition we provide a conceptual explanation of this phenomena through several di erent 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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