DirichletL-function and power series for Hurwitz zeta function

Heath-Brown D R, An asymptotic series for the mean value of DirichletL-series,Comment. Math. Helv. 56 (1981) 148–161

Katsurada M and Matsumoto K, Asymptotic expansions of the mean values of DirichletL-function,Math. Z. 208 (1991) pp 23–39

Motohashi Y, A Note on the mean value of the Zeta andL-function I,Proc. Jpn. Acad. Ser. A, vol.61 No 7 (1985), pp 222–224

Paley R E A C, Analogues of theorems concerning the ζ-function,Proc. London Math. Soc. 32 (1931).