PreprintCC BY-NC-ND 4.0arXiv
Human Exposition of Claude's 2/3 Theorem on the zeros of zeta
Abstract
We expose Claude's proof that N0(T)≥ 0.6725 N(T) where N(T) is the number of zeros of zeta satisfying 0<mathopReρ≤ T, and N0(T) the number of those zeros that are simple and on the critical line. Unconditionally it was only known that N0(T)≥ 0.4166 N(T). This proof is simpler than the previous ones and takes a different approach.
Related
- Bourgain's proof of the circular maximal theorem: an exposition
- Zeta zeros on the critical line
- More than 8/9 zeros of the Riemann zeta function are simple or on the critical line
- One-level density of zeros of the Riemann zeta function weighted by its special values
- On the distribution of the zeros of the Euler double zeta-function ζ2(s,s)
BibTeX
@misc{reyna2026human,
title = {{Human Exposition of Claude's 2/3 Theorem on the zeros of zeta}},
author = {J. Arias de Reyna},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.24612},
eprint = {2610.24612},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.24612},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Human Exposition of Claude's 2/3 Theorem on the zeros of zeta
AU - J. Arias de Reyna
PY - 2026
DA - 2026/10/17
PB - arXiv
DO - 10.48550/arxiv.2610.24612
UR - https://arxiv.org/abs/2610.24612
AB - We expose Claude's proof that N_0(T)≥ 0.6725 N(T) where N(T) is the number of zeros of zeta satisfying 0<mathopReρ≤ T, and N_0(T) the number of those zeros that are simple and on the critical line. Unconditionally it was only known that N_0(T)≥ 0.4166 N(T). This proof is simpler than the previous ones and takes a different approach.
ER -