PreprintarXiv licencearXiv
Non-vanishing of symmetric square L-functions in the weight aspect
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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BibTeX
@misc{balkanova2026nonvanishing,
title = {{Non-vanishing of symmetric square $L$-functions in the weight aspect}},
author = {Olga Balkanova and Dmitry Frolenkov},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09942},
eprint = {2609.09942},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09942},
}
RIS
TY - UNPB
TI - Non-vanishing of symmetric square L-functions in the weight aspect
AU - Olga Balkanova
AU - Dmitry Frolenkov
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.09942
UR - https://arxiv.org/abs/2609.09942
AB - 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%.
ER -