Abstract
The periodic zeta-function is defined by the ordinary Dirichlet series with periodic coefficients. In the paper, joint universality theorems on the approximation of a collection of analytic functions by nonlinear shifts of periodic zeta-functions with multiplicative coefficients are obtained. These theorems do not use any independence hypotheses on the coefficients of zeta-functions.
Highlights
After a famous Voronin’s work [27], it is known that the majority of classical zeta- and L-functions have the universality property, i.e., they approximate wide classes of analytic functions
Voronin considered approximation of analytic functions defined on D by shifts ζ(s + iτ ), τ ∈ R
The present paper is devoted to the joint universality for periodic zeta-functions
Summary
After a famous Voronin’s work [27], it is known that the majority of classical zeta- and L-functions have the universality property, i.e., they approximate wide classes of analytic functions. The first joint universality results were obtained for Dirichlet L-functions in [1, 2, 6, 26], see [11, 15, 25]. R, Kj ∈ K and fj(s) ∈ H0(Kj), for every ε > 0, lim inf meas T →∞ T τ ∈ [0, T ]: sup sup 1 j r s∈Kj. Pankowski in [23] proposed a new way of joint universality for Dirichlet L-functions by using different shifts for L-functions with arbitrary characters χ1, . The present paper is devoted to the joint universality for periodic zeta-functions. Denote by U1(T0), T0 > 0, the class of real increasing to ∞ continuously differentiable functions γ(τ ) with monotonic derivative γ (τ ) on [T0, ∞) such that γ(2τ ) × maxτ u 2τ 1/γ (u) τ as τ → ∞. A ∈ B Hr(D) , and PTr (A) d=ef τ ∈ [T0, T ]: ζ s + iγ(τ ); a as T → ∞
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
