Extreme values of Dirichlet $L$-functions on the critical line with a growing prime modulus
Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Dong, Zikang, Yang, Qiyu, Zhao, Shengbo
Institutions: Soochow University, Henan Normal University, Tongji University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G2332614614
OpenAlex ID: W7220384495