Abstract:We prove a functional limit theorem in a space of analytic functions for the random Dirichlet series D(α; z) = ∑ n≥2 (log n) α (η n + iθ n )/n z , properly scaled and normalized, where (η n , θ n ) n∈N is a sequence of independent copies of a centered R 2 -valued random vector (η, θ ) with a finite second moment and α > −1/2 is a fixed real parameter. As a consequence, we show that the point processes of complex and real zeros of D(α; z) converge vaguely, thereby obtaining a universality result. In the real ca… Show more
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