Universality of the zeta function in short intervals

2025/02/21 by Lee, Yoonbok, Pańkowski, Łukasz
#11M41 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2502.15364

Abstract

We improve the universality theorem of the Riemann zeta-function in short intervals by establishing universality for significantly shorter intervals [T,T+H]. Assuming the Riemann Hypothesis, we prove that universality in such short intervals holds for H=(log T)^B with an explicitly given B>0. Unconditionally, we show that for the same H the set of real numbers τ∈[T,T+H] such that ζ(s+iτ) approximates an arbitrary given analytic function has a positive upper density.

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