The fourth moment of Dirichlet L-functions along the critical line

Abstract

Abstract For a positive integer q ≢ 2 ⁢ ( mod ⁢ 4 ) {q\not\equiv 2~{}(\mathrm{mod}~{}4)} , this work considers the fourth moment of Dirichlet L-functions averaged over both t ∈ [ 0 , T ] {t\in[0,T]} and primitive characters modulo q. An asymptotic formula with a power saving from both the q-aspect and the t-aspect in the error term is obtained.