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arXiv · 2607.21532

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

Hung M. Bui·Alexandra Florea·Micah B. Milinovich
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Abstract

Under the Generalized Riemann Hypothesis, we prove a weighted central limit theorem for the joint distribution of four Dirichlet $L$--functions at the central point, twisted by the family of primitive characters to a large prime modulus. As an application, we show that a positive proportion of the characters in the family yield four central values that are simultaneously large, and a positive proportion yield values that are simultaneously nonzero and small.

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Hung M. Bui, Alexandra Florea, Micah B. Milinovich. 2026-07-23. Simultaneous non-vanishing of Dirichlet $L$--functions, II: Weighted central limit theorem. https://arxiv.org/abs/2607.21532

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