Counting zeros of Artin $L$-functions
Number Theory
2026-06-30 v1
Abstract
In this article, assuming Artin's (holomorphy) conjecture, we establish an explicit asymptotic formula for the number of non-trivial zeros, up to any given height , of Artin -functions. As a consequence, our result yields an unconditional explicit zero-counting formula for Hecke -functions over any number field. In addition, our result improves the recent work of Amberger on Dedekind and Riemann zeta functions and the previous work of Bennett-Martin-O'Bryant-Rechnitzer on Dirichlet -functions for sufficiently large .
Cite
@article{arxiv.2606.31441,
title = {Counting zeros of Artin $L$-functions},
author = {Chiara Bellotti and Peng-Jie Wong},
journal= {arXiv preprint arXiv:2606.31441},
year = {2026}
}