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arXiv · 2609.09942

Non-vanishing of symmetric square $L$-functions in the weight aspect

Olga Balkanova·Dmitry Frolenkov
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Abstract

We prove a new asymptotic formula for the second moment of symmetric square L-functions in the weight aspect on average. This result implies that the associated L-function is non-vanishing at the central point for at least 76.69% of holomorphic Hecke cusp forms of bounded weight, improving the previous bound of 70.37%.

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Olga Balkanova, Dmitry Frolenkov. 2026-09-09. Non-vanishing of symmetric square $L$-functions in the weight aspect. https://arxiv.org/abs/2609.09942

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