Higher moments of primitive Dirichlet L-functions

Establish asymptotic formulas for the 2k-th moments of primitive Dirichlet L-functions at the central point for every integer k greater than or equal to 3.

Background

The paper discusses moments of primitive Dirichlet L-functions averaged over primitive characters modulo q. It states that asymptotic formulas are currently known only for the second and fourth moments, while the higher-moment regime remains beyond the methods available in the paper.

This is a broad unresolved problem concerning the extension of known moment asymptotics to all higher powers, and it is presented as a fundamental problem in the study of Dirichlet L-functions.

References

For $k\geq 3$, it appears to be beyond the reach of currently available methods and obtaining an asymptotic formula remains a fundamental open problem.

— The second moment of twisted modular $L$-functions and Dirichlet $L$-functions at the central point  (2608.25812 - Chen et al., 26 Aug 2026) in Section 1, Introduction