PreprintCC BY 4.0arXiv
Central non-vanishing of Dirichlet L-functions
Abstract
We prove that, for every sufficiently large modulus qnot≡2bmod4, at least 3/8−o(1) of the primitive Dirichlet characters χ modulo q have L(1/2,χ)≠0. We also establish stronger proportions for moduli q satisfying certain arithmetic conditions.
Related
- Non-vanishing of central values of angular Hecke L-functions
- Vanishing orders of Dirichlet solutions to the Schrödinger equation in dimensions three and higher
- Non-vanishing of symmetric square L-functions in the weight aspect
- The First Moment of Dirichlet L-functions over Generators of the Character Group
- Large values of cubic and quartic Dirichlet L-functions of prime moduli
BibTeX
@misc{durkan2026central,
title = {{Central non-vanishing of Dirichlet $L$-functions}},
author = {Benjamin Durkan and Andrew Pearce-Crump},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.06167},
eprint = {2609.06167},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06167},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Central non-vanishing of Dirichlet L-functions
AU - Benjamin Durkan
AU - Andrew Pearce-Crump
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2609.06167
UR - https://arxiv.org/abs/2609.06167
AB - We prove that, for every sufficiently large modulus qnot≡2bmod4, at least 3/8−o(1) of the primitive Dirichlet characters χ modulo q have L(1/2,χ)≠0. We also establish stronger proportions for moduli q satisfying certain arithmetic conditions.
ER -