Abstract
We prove that every collection of analytic functions (f1(s), . . . , fr(s)) defined on the right-hand side of the critical strip can be simultaneously approximated by shifts of Hurwitz zeta-functions (ζ(s + iγκh, α1), … , ζ(s + iγκh, αr)), h > 0, where 0 < γ1 ≤ γ2 ≤ … are the imaginary parts of nontrivial zeros of the Riemann zeta-function ζ(s). We use the weak form of the Montgomery pair correlation conjecture and the linear independence over ℚ of the set {log(m + αj) : m ∈ ℕ0, j = 1, … , r}.
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Dedicated to Professors Antanas Laurinčikas and Eugenijus Manstavičius on the occasion of their 70th birthdays
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Macaitienė, R., Šiaučiūnas, D. Joint universality of Hurwitz zeta-functions and nontrivial zeros of the Riemann zeta-function. Lith Math J 59, 81–95 (2019). https://doi.org/10.1007/s10986-019-09423-2
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DOI: https://doi.org/10.1007/s10986-019-09423-2