PreprintCC BY 4.0arXiv
The sixth moment of a degree two L-function of arbitrary level
Abstract
Let f be a primitive holomorphic cusp form of arbitrary weight, level and nebentypus. We prove ∫0T|L(1/2+it,f)|6 dt≪f,εT2+ε, extending Jutila's level-one theorem. The new ingredient is a large sieve comparing the stationary phases in the Booker-Milinovich-Ng transformation at different heights. Applications include moments of order T1+ε on every line to the right of the critical line, Ω(T4/35−ε) simple zeros, zero density estimates, and bounds for cubic-field power sums, shifted convolution sums and the general divisor problem.
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BibTeX
@misc{pearcecrump2026sixth,
title = {{The sixth moment of a degree two $L$-function of arbitrary level}},
author = {Andrew Pearce-Crump},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.39706},
eprint = {2609.39706},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.39706},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The sixth moment of a degree two L-function of arbitrary level
AU - Andrew Pearce-Crump
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2609.39706
UR - https://arxiv.org/abs/2609.39706
AB - Let f be a primitive holomorphic cusp form of arbitrary weight, level and nebentypus. We prove ∫_0^T|L(1/2+it,f)|^6 dt≪_f,εT^2+ε, extending Jutila's level-one theorem. The new ingredient is a large sieve comparing the stationary phases in the Booker-Milinovich-Ng transformation at different heights. Applications include moments of order T^1+ε on every line to the right of the critical line, Ω(T^4/35−ε) simple zeros, zero density estimates, and bounds for cubic-field power sums, shifted convolution sums and the general divisor problem.
ER -