Mathematics – General Mathematics
Scientific paper
2011-02-16
Mathematics
General Mathematics
The basic moment of the work is using of a new measure in infinite dimensional unite cube different from Haar or product Lebes
Scientific paper
In this paper we study the mean values and zeroes of Dirichlet series of a view $\sum_{n}a_n n^{-s}$ with complex coefficients. There was introduced some class of Dirichlet series including such widely used series as the Riemann zeta-function, Dirichlet L-functions and ets. A new point of view is introduced in defining of a half plane of mean values. It was proven that in the half plane 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 of Lindel\"of Hypothesis is true. If, in addition, the Dirichlet series f(s) belongs to this class with the function f^(-1)(s) then the half plane of mean values was proved to be free from the zeroes.
No associations
LandOfFree
On mean values and zeroes of Dirichlet series does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On mean values and zeroes of Dirichlet series, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On mean values and zeroes of Dirichlet series will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-417415