Non-vanishing of the symmetric square L -function at the central point
Abstract
Using the mollifier method, we show that, for a positive proportion of holomorphic Hecke eigenforms of level one and weight bounded by a large enough constant, the associated symmetric square L -function does not vanish at the central point of its critical strip. We note that our proportion is the same as that found by other authors for other families of L -functions also having symplectic symmetry type.