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<p>The paper is devoted to the study of the Selberg–Steuding class <i>𝒮</i>. The main result shows that analytic functions are simultaneously approximable by discrete shifts of the <i>L</i>-function from <i>𝒮</i>, and we prove a similar result on the universality in the density terms. Moreover, in such shifts the imaginary parts <i>γ</i><sub><i>k</i></sub> of the nontrivial zeros of the Riemann zeta-function <i>ζ</i> are involved. In the proof, we use a weaker version of the Montgomery pair correlation conjecture. The results extend a one-dimensional theorem of the first author.</p>

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Joint discrete universality in the Selberg–Steuding class and nontrivial zeros of the Riemann zeta-function

  • 期刊论文

  • 发表日期：

    2026年1月26日

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  • Roma Kačinskaitė,
  • Benjaminas Togobickij

摘要

The paper is devoted to the study of the Selberg–Steuding class 𝒮. The main result shows that analytic functions are simultaneously approximable by discrete shifts of the L-function from 𝒮, and we prove a similar result on the universality in the density terms. Moreover, in such shifts the imaginary parts γk of the nontrivial zeros of the Riemann zeta-function ζ are involved. In the proof, we use a weaker version of the Montgomery pair correlation conjecture. The results extend a one-dimensional theorem of the first author.