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Mixed moment of GL(2) and GL(3) L-functions in the level aspect
Abstract
In this paper, we establish an asymptotic formula of mixed moments of L(1/2,f) and L(1/2,sym2 f) for cusp forms f of weight k, prime level q and real primitive nebentypus χ modulo q in the level aspect with a power-saving error term. As an application, we deduce the simultaneous non-vanishing of $L(1/2, f)$ and L(1/2,sym2 f) for sufficiently large prime levels.
Versions
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BibTeX
@misc{liu2026mixed,
title = {{Mixed moment of $GL(2)$ and $GL(3)$ $L$-functions in the level aspect}},
author = {Zhiwei Liu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.16893},
eprint = {2609.16893},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.16893},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Mixed moment of GL(2) and GL(3) L-functions in the level aspect
AU - Zhiwei Liu
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.16893
UR - https://arxiv.org/abs/2609.16893
AB - In this paper, we establish an asymptotic formula of mixed moments of L(1/2,f) and L(1/2,sym^2 f) for cusp forms f of weight k, prime level q and real primitive nebentypus χ modulo q in the level aspect with a power-saving error term. As an application, we deduce the simultaneous non-vanishing of $L(1/2, f)$ and L(1/2,sym^2 f) for sufficiently large prime levels.
ER -