Non universality on the critical line
Number Theory
2016-06-09 v2
Abstract
We prove that the Riemann zeta-function is not universal on the critical line by using the fact that the Hardy Z-function is real, and some elementary considerations. This is a related to a recent result of Garunkstis and Steuding. We also prove conditional and partial results for non universality on the lines Re(s)=\sigma for 0<\sigma<1/2 and together with our recent result for non universality on the line Re(s)=1 it will mostly answer the question of on what lines the zeta-function is universal.
Keywords
Cite
@article{arxiv.1207.4927,
title = {Non universality on the critical line},
author = {Johan Andersson},
journal= {arXiv preprint arXiv:1207.4927},
year = {2016}
}
Comments
v1: 15 pages v2: 14 pages. Proved Lemma 1 with a new method after Aleksandar Ivic (thanks!) found mistakes in the previous proof + minor edits