Year: 2026
Type: preprint
Abstract: We study the nonvanishing of central values of ray class $L$-functions over a fixed imaginary quadratic field $K$. We prove that, as $\mathrm{N}(\mathfrak f)$ tends to infinity, at least a proportion $1/3-\mathsf{o}_K(1)$ of the primitive ray class characters $χ$ modulo $\mathfrak f$ satisfy $L(1/2,χ)\neq 0$. Our proof adapts the classical mollifier method to the ray class setting and establishes asymptotic formulas for the first and second mollified moments.
Source: arXiv (Cornell University)
Authors: Ye, Thurman, Zhuang, Xu
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Mitacs
OpenAlex ID: W7213508604