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PreprintCC0arXiv

Extreme values of Dirichlet L-functions on the critical line with a growing prime modulus

  • Zikang Dong
  • Qiyu Yang
  • Shengbo Zhao
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Abstract

In this paper, we obtain extreme values of Dirichlet L-functions on the critical line with a growing prime modulus. Our result yields a larger lower bound for extreme values than that from Soundararajan's classical resonance method. Consequently, we show that one branch of the dichotomy established by Bondarenko, Darbar, Hagen, Heap, and Seip (2023) can be realized for this family of Dirichlet L-functions. The proof relies on the resonance method together with precise estimates for GCD sums.

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Cite

BibTeXRIS
BibTeX
@misc{dong2026extreme,
  title = {{Extreme values of Dirichlet $L$-functions on the critical line with a growing prime modulus}},
  author = {Zikang Dong and Qiyu Yang and Shengbo Zhao},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.02709},
  eprint = {2610.02709},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.02709},
  note = {CC0},
}
RIS
TY  - UNPB
TI  - Extreme values of Dirichlet L-functions on the critical line with a growing prime modulus
AU  - Zikang Dong
AU  - Qiyu Yang
AU  - Shengbo Zhao
PY  - 2026
DA  - 2026/10/02
PB  - arXiv
DO  - 10.48550/arxiv.2610.02709
UR  - https://arxiv.org/abs/2610.02709
AB  - In this paper, we obtain extreme values of Dirichlet L-functions on the critical line with a growing prime modulus. Our result yields a larger lower bound for extreme values than that from Soundararajan's classical resonance method. Consequently, we show that one branch of the dichotomy established by Bondarenko, Darbar, Hagen, Heap, and Seip (2023) can be realized for this family of Dirichlet L-functions. The proof relies on the resonance method together with precise estimates for GCD sums.
ER  -