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Weyl Bounds for GL2× GL2 Rankin--Selberg L-functions via Short Spectral Moments
Abstract
Let f and g be Hecke--Maass cusp forms of SL2(ℤ), with spectral parameters tf and tg, respectively. Let T be a large parameter and put L = |T−tg|. We prove the Lindelöf-on-average estimate ∑ |tf−T|≤ H |L (1/2,f⊗ g)|2 ≪ε T1+εH, uniformly in the range T1/3+ε≪ H, HTε≪ L≤ T. As an immediate consequence, in the generic range when both |tg| and L are of size T, we obtain the Weyl bound L (1/2,f⊗ g) ≪ε C(f× g)1/6+ε.
Related
BibTeX
@misc{wang2026weyl,
title = {{Weyl Bounds for $\operatornameGL_2\times \operatornameGL_2$ Rankin--Selberg $L$-functions via Short Spectral Moments}},
author = {Zihao Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27804},
eprint = {2610.27804},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27804},
}
RIS
TY - UNPB
TI - Weyl Bounds for GL_2× GL_2 Rankin--Selberg L-functions via Short Spectral Moments
AU - Zihao Wang
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.27804
UR - https://arxiv.org/abs/2610.27804
AB - Let f and g be Hecke--Maass cusp forms of SL_2(ℤ), with spectral parameters t_f and t_g, respectively. Let T be a large parameter and put L = |T−t_g|. We prove the Lindelöf-on-average estimate ∑_ |t_f−T|≤ H |L (1/2,f⊗ g)|^2 ≪_ε T^1+εH, uniformly in the range T^1/3+ε≪ H, HT^ε≪ L≤ T. As an immediate consequence, in the generic range when both |t_g| and L are of size T, we obtain the Weyl bound L (1/2,f⊗ g) ≪_ε C(f× g)^1/6+ε.
ER -