PreprintCC BY 4.0arXiv
Large values of the Hurwitz zeta function with rational parameter
Abstract
In this paper, we establish lower bounds for large values of the Hurwitz zeta function with rational parameter when the real part σ∈ [1/2,1]. These results improve the earlier results of Ramachandra and Sankaranarayanan in 1989. On the critical line, our result recovers the corresponding lower bound of de la Bretèche and Tenenbaum (2019) for the Riemann zeta function, while for 1/2< σ≤ 1, our lower bounds attain the same order as the corresponding lower bounds for large values of the Riemann zeta function. Our proofs are based on the resonance method.
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BibTeX
@misc{yang2026large,
title = {{Large values of the Hurwitz zeta function with rational parameter}},
author = {Qiyu Yang and Shengbo Zhao and Guang-Liang Zhou},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.25985},
eprint = {2609.25985},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.25985},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Large values of the Hurwitz zeta function with rational parameter
AU - Qiyu Yang
AU - Shengbo Zhao
AU - Guang-Liang Zhou
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.25985
UR - https://arxiv.org/abs/2609.25985
AB - In this paper, we establish lower bounds for large values of the Hurwitz zeta function with rational parameter when the real part σ∈ [1/2,1]. These results improve the earlier results of Ramachandra and Sankaranarayanan in 1989. On the critical line, our result recovers the corresponding lower bound of de la Bretèche and Tenenbaum (2019) for the Riemann zeta function, while for 1/2< σ≤ 1, our lower bounds attain the same order as the corresponding lower bounds for large values of the Riemann zeta function. Our proofs are based on the resonance method.
ER -