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International Mathematics Research Notices (2002) 2002:1723-1738 , doi:10.1155/S107379280211110X
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Copyright © 2002 Hindawi Publishing Corporation. All rights reserved.

Integrals of Eisenstein series and derivatives of L-functions

Scott Ahlgren, Bruce C. Berndt, Ae Ja Yee and Alexandru Zaharescu

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 L-function 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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