PreprintarXiv licencearXiv
Zero density theorems for short intervals
Abstract
We provide explicit bounds on the number of zeros for ζ in short intervals near the edge of the critical strip. Ultimately we show that even in short intervals a positive proportion of zeros will not be near the edge of the critical strip. For example with h>100 and t>10100 the proportion of zeros of ζ with imaginary part in [t−h,t+h] which have real part in [1/16,15/16] is at least 13% and a positive proportion is already obtained at t>1043.
Related
- Halász theorems for Gaussian ideals in sectors and short intervals
- Zero density in short strips and short-interval bounds toward Hypothesis S
- Subvariety intervals and limit varieties of zero extensions of mirror-word semirings
- Lattice points close to a smooth curve and squarefull numbers in short intervals. II
- Almost k-th powers in short intervals
BibTeX
@misc{fiori2026zero,
title = {{Zero density theorems for short intervals}},
author = {Andrew Fiori},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.22624},
eprint = {2609.22624},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.22624},
}
RIS
TY - UNPB
TI - Zero density theorems for short intervals
AU - Andrew Fiori
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.22624
UR - https://arxiv.org/abs/2609.22624
AB - We provide explicit bounds on the number of zeros for ζ in short intervals near the edge of the critical strip. Ultimately we show that even in short intervals a positive proportion of zeros will not be near the edge of the critical strip. For example with h>100 and t>10^100 the proportion of zeros of ζ with imaginary part in [t−h,t+h] which have real part in [1/16,15/16] is at least 13% and a positive proportion is already obtained at t>10^43.
ER -