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

2025/04/16 by Xiaojie Wu, Qin, Xinhua, Wu, Xiaosheng
Mathematics · #11M20 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2504.11916

openalex publication_date 2025/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

Citations

• Non-vanishing for cubic Hecke L-functions
• Non-vanishing of Dirichlet L-functions with smooth conductors
• Bounds on bilinear forms with Kloosterman sums
• Exceptional characters and nonvanishing of Dirichlet L-functions
• Nonvanishing of Dirichlet L-functions, II
• Nonvanishing of Dirichlet L-functions, II
• Nonvanishing of Dirichlet L-functions
• Gaussian distribution for the divisor function and Hecke eigenvalues in arithmetic progressions
• Nonvanishing of quadratic Dirichlet L-functions at s=1/2
• Nonvanishing of Quadratic Dirichlet L-Functions at S = &#189
• More than two fifths of the zeros of the Riemann zeta function are on the critical line.

Related

• Nonvanishing of Dirichlet L-functions, II
• On the non-vanishing of Dirichlet L-functions at the central point
• Non-vanishing of Dirichlet L-functions with smooth conductors
• Vanishing of Dirichlet L-functions at the central point over function fields
• Non-vanishing of Cubic Dirichlet L-Functions over the Eisenstein Field