Twisted second moment of primitive cubic L-functions

2025/06/17 by Hong, Ziwei, Zheng, Zhiyong
#11L05 #11L40 #11M06 #11M41 #11N37 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2506.14656

Abstract

We investigate the mean value of the twisted second moment of primitive cubic L-functions over \mathbbF_q(T) in the non-Kummer setting. Specifically, we study the sum ∑_\substackχ primitive cubic
genus(χ)=gχ(h₁)χ(h₂)|L_q((1)/(2), χ)|², where L_q(s,χ) denotes the L-function associated with primitive cubic character χ. Employing a double Dirichlet series approach, we establish an error term of size

Citations

• Nonvanishing of L--functions associated to fixed order characters over function fields
• The second moment of cubic Dirichlet L-functions over function fields
• The first moment of central value of primitive quartic L-functions with fixed genus
• Mean value of cubic L-funcitons with fixed genus
• Non-vanishing for cubic Hecke L-functions
• Mollified Moments of Cubic Dirichlet L-Functions over the Eisenstein Field
• The Ratios conjecture for real Dirichlet characters and multiple Dirichlet series
• Non-vanishing for cubic L--functions
• On the distribution of the rational points on cyclic covers in the absence of roots of unity

Related

• Mean value of cubic L-funcitons with fixed genus
• The first moment of central value of primitive quartic L-functions with fixed genus
• A Note on Twisted Moments of Dirichlet L-functions
• Twisted first moment of central values of primitive quadratic Dirichlet L-functions
• The second moment of cubic Dirichlet L-functions over function fields