Zeta Values and Differential Operators on the Circle Original Research Article

The Fock representation of the Virasoro Lie algebra is extended to a larger graded Lie subalgebra of the algebra of differential operators on the circle. The central cocycle is related to values of the Riemann Zeta function at odd negative integers. The corresponding generating function is related to Eisenstein series forSL2(Z). An analogous result is obtained for values ofL-series associated to even Dirichlet characters using differential operators of infinite order.