Year: 2025
Type: preprint
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 $\tau\in[T,T+H]$ such that $\zeta(s+i\tau)$ approximates an arbitrary given analytic function has a positive upper density.
Source: arXiv (Cornell University)
Authors: Lee, Yoonbok, Pa\'nkowski, {\L}ukasz
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6979336259
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