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Non-vanishing of Dirichlet $L$-functions at the Central Point

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arxiv 2504.11916 v2 pith:437XCFLW submitted 2025-04-16 math.NT

Xinhua Qin , Xiaosheng Wu This is my paper · ORCID
classification math.NT
keywords centraldirichletnon-vanishingcharactersfracfrac12functionsgeneral
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abstract

We prove that for at least $\frac{7}{19}$ of the primitive Dirichlet characters $\chi$ with large general modulus, the central value $L(\frac12,\chi)$ is non-vanishing.

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Cited by 2 Pith papers

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  1. Simultaneous nonvanishing of Dirichlet $L$-functions in Galois orbits

    math.NT 2025-07 conditional novelty 7.0 of 10

    Under GRH, in every Galois orbit modulo p^k, a positive proportion of characters chi satisfy L(1/2, chi eta1) L(1/2, chi eta2) != 0 for distinct imprimitive twists eta1, eta2.

  2. Simultaneous non-vanishing of Dirichlet $L$--functions, II: Weighted central limit theorem

    math.NT 2026-07 conditional novelty 6.0 of 10

    For primitive characters modulo a large prime, under GRH, the four twisted central L-value logarithms are asymptotically independent standard Gaussians under a weighted measure.

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