PreprintCC BY 4.0arXiv
An Omega result for partial sums of the Riemann zeta function
Abstract
In this paper, we establish an Omega result for partial sums of the Riemann zeta function on the 1-line. Our work relies on the long resonance method and an effective asymptotic formula for smooth numbers. For sufficiently long partial sums, our result approaches the work obtained by Aistleitner, Mahatab and Munsch in 2019.
Related
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BibTeX
@misc{yang2026omega,
title = {{An Omega result for partial sums of the Riemann zeta function}},
author = {Qiyu Yang and Shengbo Zhao},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18938},
eprint = {2609.18938},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18938},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - An Omega result for partial sums of the Riemann zeta function
AU - Qiyu Yang
AU - Shengbo Zhao
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.18938
UR - https://arxiv.org/abs/2609.18938
AB - In this paper, we establish an Omega result for partial sums of the Riemann zeta function on the 1-line. Our work relies on the long resonance method and an effective asymptotic formula for smooth numbers. For sufficiently long partial sums, our result approaches the work obtained by Aistleitner, Mahatab and Munsch in 2019.
ER -