Joint discrete approximation of a pair of analytic functions by periodic zeta-functions

Abstract

In the paper, the problem of simultaneous approximation of a pair of analytic functions by a pair of discrete shifts of the periodic and periodic Hurwitz zeta-function is considered. The above shifts are defined by using the sequence of imaginary parts of non-trivial zeros of the Riemann zeta-function. For the proof of approximation theorems, a weak form of the Montgomery pair correlation conjecture is applied.

Keywords

• Hurwitz zeta-function
• non-trivial zeros of the Riemann zeta-function
• periodic zeta-function
• periodic Hurwitz zeta-function
• universality