Numerical Computations Concerning Landau-Siegel Zeros
Year: 2026
Type: preprint
Abstract: We computationally verify that if $L(s,χ)$ is a quadratic Dirichlet $L$-function modulo $q \leq 10^{10}$ then $L(σ,χ) \neq 0$ for real $σ\ge 1-1/(5\log q)$. The number of verified moduli exceeds benchmarks due to Watkins (2004), Platt (2016), and Languasco (2023) by a factor between 66 and 25,000. Our new algorithm draws from zero-free region arguments.
Source: arXiv (Cornell University)
Authors: Lu, Rick F., Zaman, Asif, Zhao, Haonan
Institution: University of Toronto
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7127596002
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