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Joint Universality for the Riemann zeta-function with general shifts

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arxiv 2312.04269 v2 pith:GM27PLCB submitted 2023-12-07 math.NT

classification math.NT
keywords generalriemannshiftsuniversalityzeta-functionjointtheoremandersson
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Laurin\v{c}ikas proposed that whether the universality theorem for the Riemann zeta-function shifted by an exponential function holds or not. This problem is solved for more general shifts by Andersson et al. In this paper, we generalize their result for the joint universality theorem for the Riemann zeta-function with general shifts using a different approach from their method.

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  1. On the value distribution of the Riemann zeta-function with general shifts

    math.NT 2026-07 conditional novelty 7.0 of 10

    The Riemann zeta-function is shown to have the universality and Bohr–Jessen distribution properties under logarithmic-power shifts (log t)^α, α>1, with quantitative discrepancy bounds.

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