English

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 T1T\geq 1, of Artin LL-functions. As a consequence, our result yields an unconditional explicit zero-counting formula for Hecke LL-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 LL-functions for sufficiently large TT.

Keywords

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}
}