Non‐vanishing of the symmetric square L‐function at the central point

By Rizwanur Khan. 2008

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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.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d903e5605ef20a80d5c28b7d8c6a06836b50d122