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arXiv · 2609.06167

Central non-vanishing of Dirichlet $L$-functions

Benjamin Durkan·Andrew Pearce-Crump
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Abstract

We prove that, for every sufficiently large modulus $q\not\equiv2\bmod4$, at least $3/8-o(1)$ of the primitive Dirichlet characters $\chi$ modulo $q$ have $L(1/2,\chi)\ne0$. We also establish stronger proportions for moduli $q$ satisfying certain arithmetic conditions.

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Benjamin Durkan, Andrew Pearce-Crump. 2026-09-05. Central non-vanishing of Dirichlet $L$-functions. https://arxiv.org/abs/2609.06167

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