Renormalization of certain integrals defining triple product L-functions

Jennifer E. Beineke

Vol. 203 (2002), No. 1, 89–114

DOI: 10.2140/pjm.2002.203.89

Abstract

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.

Milestones

Received: 25 May 2000

Revised: 30 October 2000

Published: 1 March 2002