A generalization of the Voronin theorem
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The classical Voronin universality theorem asserts that a wide class of analytic functions can be approximated by shifts of the Riemann zeta-function ζ(s + iτ), τ ∈ ℝ. In the paper, we generalize this approximation for shifts ζ(s + iφ(τ)), where 𝜑(τ) has the monotonic positive derivative such that 1/𝜑′(τ) = o(τ) and φ(2τ) × maxτ ≪ t ≪ 2τ(1/φ′(t)) ≪ τ as τ →∞.
KeywordsHaar measure limit theorem Mergelyan theorem Riemann zeta function universality
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