A Weighted Version of the Mishou Theorem

摘要

In 2007, H. Mishou obtained a joint universality theorem for the Riemann and Hurwitz zeta-functions zeta(s) and zeta(s, alpha) with transcendental parameter a on the approximation of a pair of analytic functions by shifts Ms ii), (zeta s + ir), zeta(s+ir, alpha)) tau is an element of R. In the paper, the Mishou theorem is generalized for the set of above shifts having a weighted positive lower density. Also, the case of a positive density is considered.