A weighted version of the Mishou theorem

Abstract

In 2007, H. Mishou obtained a joint universality theorem for the Riemann and Hurwitz zeta-functions ζ(s) and ζ(s,α) with transcendental parameter α on the approximation of a pair of analytic functions by shifts (ζ(s+iτ),ζ(s+iτ,α)), τ ∈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.

Keywords

• hurwitz zeta-function
• mishou theorem
• riemann zeta-function
• universality