Integrals of Eisenstein Series and Derivatives of L-functions
نویسندگان
چکیده
In his lost notebook, Ramanujan recorded a formula relating a “character analogue” of the Dedekind eta-function, the integral of a quotient of eta-functions, and the value of a Dirichlet Lfunction at s = 2. Here we derive an infinite family of formulas which includes Ramanujan’s original formula as a special case. Our results depend on a representation of values of the derivatives of Dirichlet L-functions as the limiting values of certain q-series.
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