PreprintCC BY 4.0arXiv
Nonvanishing of ray class L-functions
Abstract
We study the nonvanishing of central values of ray class L-functions over a fixed imaginary quadratic field K. We prove that, as N(f) tends to infinity, at least a proportion 1/3−oK(1) of the primitive ray class characters χ modulo f satisfy L(1/2,χ)≠ 0. Our proof adapts the classical mollifier method to the ray class setting and establishes asymptotic formulas for the first and second mollified moments.
Related
- Nonvanishing of special L-values of cusp forms on GL(2) with totally split prime power twists: without the class number hypothesis
- A formula for the elasticity of substitution of a large class of smooth utility functions
- On a class of meromorphic functions with three singular values
- On Separately Continuous Functions of the First Baire Class on Squares and Mixed Products
- Newton-type inequalities for the class of modified hyperbolic p-convex functions via Riemann-Liouville fractional integrals with numerical justifications
BibTeX
@misc{ye2026nonvanishing,
title = {{Nonvanishing of ray class $L$-functions}},
author = {Thurman Ye and Xu Zhuang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18220},
eprint = {2609.18220},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18220},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Nonvanishing of ray class L-functions
AU - Thurman Ye
AU - Xu Zhuang
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.18220
UR - https://arxiv.org/abs/2609.18220
AB - We study the nonvanishing of central values of ray class L-functions over a fixed imaginary quadratic field K. We prove that, as N(f) tends to infinity, at least a proportion 1/3−o_K(1) of the primitive ray class characters χ modulo f satisfy L(1/2,χ)≠ 0. Our proof adapts the classical mollifier method to the ray class setting and establishes asymptotic formulas for the first and second mollified moments.
ER -