Abstract
In this paper various analytic techniques are com- bined in order to study the average of a product of a Hecke L- function and a symmetric square L-function at the central point in the weight aspect. The evaluation of the second main term relies on the theory of Maa{\ss} forms of half-integral weight and the Rankin-Selberg method. The error terms are bounded using the Liouville-Green approximation.
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