Universality of -Dirichlet functions and nontrivial zeros of the Riemann zeta-function

Abstract

Abstract We prove a joint discrete universality theorem for Dirichlet -functions concerning joint approximation of a tuple of analytic functions by shifts , where is the sequence of imaginary parts of the nontrivial zeros of the Riemann zeta-function, is a fixed positive number, and are pairwise nonequivalent Dirichlet characters. We use a weak form of Montgomery’s conjecture on the correlation of pairs of zeros of the Riemann zeta-function in the analysis. Moreover, we show the universality of certain compositions of Dirichlet -functions with operators in the space of analytic functions. Bibliography: 31 titles.