Mixed moment and joint non-vanishing of GL(3)×GL(1) and GL(1) L-functions

@misc{ghosh2026mixed,
  title = {{Mixed moment and joint non-vanishing of $\mathrmGL(3)\times\mathrmGL(1)$ and $\mathrmGL(1)$ $L$-functions}},
  author = {Sayan Ghosh and Pratim Mitra},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.20792},
  eprint = {2610.20792},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.20792},
}

TY  - UNPB
TI  - Mixed moment and joint non-vanishing of GL(3)×GL(1) and GL(1) L-functions
AU  - Sayan Ghosh
AU  - Pratim Mitra
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2610.20792
UR  - https://arxiv.org/abs/2610.20792
AB  - In this article, we study the mixed-moment problem for the product of central values of two L-functions twisted by a Dirichlet character of large conductor q. Precisely, for a fixed SL_3(ℤ) Hecke-Maass cusp form π, we asymptotically evaluate the first moment, with power−saving error term for the product of central L-values L(1/2, π×χ)L(1/2, χ)̅ averaged over the full family {χ (mod q): Q≤ q≤ 2Q} of primitive Dirichlet characters modulo q. And as a consequence, we also established the simultaneous non-vanishing of the aforementioned central L-values.
ER  -