Abstract:

In this paper, we study the random Dirichlet series on the right half-plane. First, we find a better condition of coefficient and a example which this condition is the best under certain sense. Then we extend a lemma of Paley-Zygmund to-Zygmund to the cases of non-equally distributed and study the value distribution of more general random Dirichlet series with this lemma.

Key words: 　Ｒａｎｄｏｍｓｅｒｉｅ, Ｃｈａｒａｃｔｅｒｉｓｔｉｃｆｕｎｃｔｉｏｎ, Ｖａｌｕｅｄｉｓｔｒｉｂｕｔｉｏｎ