ON THE CENTRAL CRITICAL VALUE

OF THE TRIPLE PRODUCT L-FUNCTION

Siegfried Boecherer Rainer Schulze-Pillot

Abstract. We compute the central critical value of the triple product L-function associated to three cusp forms f_{1}, f_{2}, f_{3} with trivial character for groups Γ_{0}(N_{i}) with square free levels N_{i} not all of which are 1 and weights k_{i} satisfying k_{1} ≥ k_{2} ≥ k_{3} and k_{1} < k_{2} + k_{3}. This generalizes work of Gross and Kudla and gives an alternative classical proof of their results in the case N_{1} = N_{2} = N_{3} with k_{1} = k_{2} = k_{3} = 2.

Typeset by AMS-TEX