Moments and Non-Vanishing of Maass Form Symmetric Square L-Functions in Short Intervals

@misc{balkanova2026moments,
  title = {{Moments and Non-Vanishing of Maass Form Symmetric Square L-Functions in Short Intervals}},
  author = {Olga Balkanova and Dmitry Frolenkov},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.11119},
  eprint = {2609.11119},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.11119},
}

TY  - UNPB
TI  - Moments and Non-Vanishing of Maass Form Symmetric Square L-Functions in Short Intervals
AU  - Olga Balkanova
AU  - Dmitry Frolenkov
PY  - 2026
DA  - 2026/09/10
PB  - arXiv
DO  - 10.48550/arxiv.2609.11119
UR  - https://arxiv.org/abs/2609.11119
AB  - Recently, Li obtained a mean Lindelöf estimate for the cubic moment of the central values of Maass form symmetric square L-functions over short intervals (T−H, T+H) of length H ≥ T^18/19+ε. We improve this result by showing that the estimate holds for H ≫ T^6/7+ε. The key ingredient in our proof is a new asymptotic formula for the second twisted moment of Maass symmetric square L-functions. Based on this formula, we also improve the lower bound for the proportion of non-vanishing central L-values in short intervals. Previously, even under the assumption of the Lindelöf hypothesis for Dirichlet L-functions, the proportion of non-vanishing values in intervals of length H = T^β was only known to be at least (3β−1)/4. We establish an unconditional lower bound of (7β−2)/8.
ER  -