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| On the Distribution of Values of Random Dirichlet Series (II) |
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Citation： |
Sun Daochun(孙道椿),Yu Jiarong(余家荣).On the Distribution of Values of Random Dirichlet Series (II)[J].Chinese Annals of Mathematics B,1990,11(1):33~44 |
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Net amount： 910 |
Authors： |
Sun Daochun(孙道椿); Yu Jiarong(余家荣) |
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| Abstract： |
For certain Diriehlet series almost surely (a. s.) of order (R) $\rho \in (0,\infty)$ in the right-half plane, a. s. every point of the imaginary axis is a Borel point of order \rho +1 and with no finite exceptional value.
In [9, 10] we studied the distribution of values of random Diriehlet series a. s. of infinite order(R) in the right-half plane or in the whole plane and introduced the N-sequence {Z_n(w)} (n\in N_+) of random variables, a sequence of independent, symmetric and equally distributed real or complex variables of finite variance in the probability space (Q, \mathscr(A),mathscr(P)) (w\in \Omega) for which $\exsits k_0 \in N_+$ such that
$\int_{|Z|<1}{|Z_n|^{-1/k_0}\mu(dZ_n)}<\infty$
where \mu is the common measure defined by Z_n(w).The classical Rademaoher, Steinhaus and Gauss sequences are special cases of the N-sequence.
In this paper corresponding to the N-sequence we study the distribution of values of random Diriehlet series almost surely (a. s.) of finite order (R) in the right-half plane and improve some results in [6] and [7]. Here we have Borel points of an accurate order (R) and with no finite exceptional value as in the case of Borel directions in [3], the method adopted being different. We indicate corresponding results for some random Diriehlet series a. s. of finite order (R) in the whole plane. The results in this paper can be extended to the cass of (p, q) -order (R) as in [9], [10]. |
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