Joint universality of Hurwitz zeta-functions and nontrivial zeros of the Riemann zeta-function

摘要

We prove that every collection of analytic functions (f(1)(s), . . . , f(r)(s)) defined on the right-hand side of the critical strip can be simultaneously approximated by shifts of Hurwitz zeta-functions ((s+ih,(1)),...,(s+ih,(r))), h>0, where 0<(12)... are the imaginary parts of nontrivial zeros of the Riemann zeta-function (s). We use the weak form of the Montgomery pair correlation conjecture and the linear independence over of the set {log(m+(j)):mN(0),j=1,...,r}.