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In this paper we study the mean values and zeroes of Dirichlet series of aview $\sum_{n}a_n n^{-s}$ with complex coefficients. There was introduced someclass of Dirichlet series including such widely used series as the Riemannzeta-function, Dirichlet L-functions and ets. A new point of view is introducedin defining of a half plane of mean values. It was proven that in the halfplane of mean values any natural degree of the series of an inroduced class,being regular in this half plane,has a mean value. In particular, the analog ofLindel\"of Hypothesis is true. If, in addition, the Dirichlet series f(s)belongs to this class with the function f(s)^{-1} then the half plane of meanvalues was proved to be free from the zeroes.

On mean values and zeroes of Dirichlet series