Non-vanishing of the symmetric square $L$-function at the central point

Details Non-vanishing of the symmetric square $L$-function at the central point Non-vanishing of the symmetric square $L$-function at the central point

2008-03-12

arxiv.org/abs/0803.1870v3

Mathematics

Number Theory

29 pages

Scientific paper

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.

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