Central non-vanishing of Dirichlet $L$ -functions

Benjamin Durkan, Andrew Pearce-Crump

Source record

Source: arXiv

Published: Sep 5, 2026

arXiv: 2609.06167

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Source abstract

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

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Central non-vanishing of Dirichlet $L$-functions — Mathematical Frontier Network