THE VALUE DISTRIBUTION OF RANDOM DIRICHLET SERIES ON THE RIGHT HALF PLANE (II)

Kahane has studied the value distribution of the Gauss-Taylor series ∑n=0∞αnXnzn, where {Xn} is a complex Gauss sequence and ∑n=1∞‖αn‖2=∞. In this paper, by transforming the right half plane into the unit disc and setting up some important inequalities, the value distribution of the Dirichlet series ∑n=0∞Xne−λnS is studied where {Xn} is a sequence of some non-degenerate independent random variable satisfying conditions: EXn=0;∑n=0∞E‖Xn‖2=∞;∀n∈N,Xn or ReXn or ImXn of bounded density. There exists α > 0 such that ∀n:α2E‖Xn‖2≤E2‖Xn‖