Value distribution of general Dirichlet series. V (Q1881774)

Let \(s\) be a complex variable; then the series \(f_j(s)=\sum_{m=1}^\infty a_{mj}\exp(-s\lambda_m)\) is called a general Dirichlet series. In the present paper, the authors prove a joint universality theorem (in the sense of Voronin) for a family of general Dirichlet series \(f_j(s)\) subject to certain, mostly natural, conditions on the arithmetic of the set of exponents \(\lambda_m\) and the analytic behavior of \(f_j(s)\). One of the main ingredients in the proof is the limit theorem for weakly convergent probability measures from the authors' paper [On joint distribution of general Dirichlet series, Nonlinear Anal., Model. Control 8, No. 2, 27--39 (2003; Zbl 1050.30004)]. Part IV, cf. ibid. 43, No. 3, 281--294 (2003; Zbl 1067.11056).