Year: 2026
Type: preprint
Abstract: We consider Dirichlet $L$-functions $L(s, χ)$ where $χ$ is a quadratic character to modulus $q$. We show that for $χ$ even (resp. odd) $L(σ, χ)\neq 0$ for all $σ>0$ provided that $q\leq 10^{9}$ (resp. $q\leq 10^{10})$. In particular, this result rules out Siegel--Landau zeros for such $L$-functions. Combined, these results improve on previous work by nearly four orders of magnitude. We also list some applications of this work.
Source: arXiv (Cornell University)
Authors: Platt, Dave, Trudgian, Tim
Institutions: University of Bristol, UNSW Canberra
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: University of Bristol
OpenAlex ID: W7223228374