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arXiv · 2606.31441

Counting zeros of Artin $L$-functions

Chiara Bellotti·Peng-Jie Wong
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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 $T\geq 1$, of Artin $L$-functions. As a consequence, our result yields an unconditional explicit zero-counting formula for Hecke $L$-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 $L$-functions for sufficiently large $T$.

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Chiara Bellotti, Peng-Jie Wong. 2026-06-30. Counting zeros of Artin $L$-functions. https://arxiv.org/abs/2606.31441

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