The main object of this paper is the mean square Ih(s) of higher derivatives of Hurwitz zeta functions ζ(s,α). We shall prove asymptotic formulas for Ih(1/2 + it) as t → + +∞ with the coefficients in closed expressions (Theorem 1). We also prove a certain explicit formula for Ih(1/2 + it) (Theorem 2), in which the coefficients are, in a sense, not explicit. However, one merit of this formula is that it contains sufficient information for obtaining the complete asymptotic expansion for Ih(1/2 + it) when h is small. Another merit is that Theorem 1 can be strengthened with the aid of Theorem 2 (see Theorem 3). The fundamental method for the proofs is Atkinson's dissection argument applied to the product ζ(u,α)ζ(v,α) with the independent complex variables u and v.
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