Vol. 203, No. 1, 2002

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Renormalization of certain integrals defining triple product L-functions

Jennifer E. Beineke

Vol. 203 (2002), No. 1, 89–114

We obtain special values results for the triple product L-function attached to a Hilbert modular cuspidal eigenform over a totally real quadratic number field and an elliptic modular cuspidal eigenform, both of level one and even weight. Replacing the elliptic modular cusp form by a specified Eisenstein series, we renormalize the integral defining the triple product L-function in order to obtain an integral representation for a product of Asai L-functions. We hope in further work to extend these results to triple-product L-functions attached to automorphic representations and then study the critical values of this renormalized triple product.

Received: 25 May 2000
Revised: 30 October 2000
Published: 1 March 2002
Jennifer E. Beineke
Department of Mathematics
Trinity College
Hartford, CT 06106
Western New England College
Springfield, MA 01119