@article{oai:nagoya.repo.nii.ac.jp:00008536, author = {EGAMI, SHIGEKI and MATSUMOTO, KOHJI}, issue = {1}, journal = {Journal of the London Mathematical Society}, month = {Aug}, note = {Let ζ(s,α) be the Hurwitz zeta function with parameter α. Power mean values of the form ∑^q_a=1ζ(s,α/q)^h or ∑^q_a=1|ζ(s,α/q)|^2h are studied, where q and h are positive integers. These mean values can be written as linear combinations of, ∑^q_a=1 ζ_r(s_1,...,s_r;a/q), where ζ_r(s_1,...,s_r;α)is a generalization of Euler-Zagier multiple zeta sums. The Mellin-Barnes integral formula is used to prove an asymptotic expansion of ∑^q_a=1ζ_r(s_1,...,s_r;a/q) with respect to q. Hence a general way of deducing asymptotic expansion formulas for ∑^q_a=1ζ(s,α/q)^h and ∑^q_a=1|ζ(s,α/q)|^2h is obtained. In particular, the asymptotic expansion of ∑^q_a=1ζ(1/2,a/q)^3 with respect to q is written down.}, pages = {41--60}, title = {ASYMPTOTIC EXPANSIONS OF MULTIPLE ZETA FUNCTIONS AND POWER MEAN VALUES OF HURWITZ ZETA FUNCTIONS}, volume = {66}, year = {2002} }