In this paper we are concerned
with mean value theorems for the summatory functions of a class of Dirichlet
series. This class of Dirichlet series is a class of Dirichlet series satisfying
functional equations involving multiple gamma factors. If f(s) =∑a(n)λn−s is a
Dirichlet series satisfying such a functional equation and E(x) is the associated
error term (see (1.2) and (1.4), respectively), then we prove 0-estimates
for
(1)
and
(2)
in the latter case when λn= n. The results we get for (1) improve known results in
some cases. Also the general result (1) is applicable in cases where a similar result of
Chandrasekharan and Narasimhan is not.
