Fractional Moments of Dirichlet $L$-Functions

D. R. Heath-Brown

Let $k$ be a positive real number, and let $M_k(q)$ be the sum of $|L(\frac{1}{2},\chi ){|}^{2k}$ over all non-principal characters to a given modulus $q$. We prove that $M_k(q)\ll_k ϕ(q)(\…