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

Antun Milas
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Abstract

We study relationships between spinor representations of certain Lie algebras and Lie superalgebras of differential operators on the circle and values of $ζ$--functions at the negative integers. By using formal calculus techniques we discuss the appearance of values of $ζ$--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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Antun Milas. 2003-03-12. Formal differential operators, vertex operator algebras and zeta--values, I. https://arxiv.org/abs/math/0303152

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