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

2026/07/23 by Hung M. Bui, Alexandra Florea, Micah B. Milinovich
#math.NT

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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.

Related

• Weighted central limit theorems for central values of L-functions
• Non-vanishing of Dirichlet L-functions at the Central Point
• Conditional estimates on the argument of Dirichlet L-functions with applications to low-lying zeros
• The fourth moment of Dirichlet L-functions at the central value
• Simultaneous large values and dependence of Dirichlet L-functions in the critical strip