An Explicit Lower Bound for the Proportion of Isolated Zeros of the Riemann Zeta Function
Year: 2026
Type: preprint
Abstract: We consider the full sequence of nontrivial zeros of the Riemann zeta function with positive ordinate, counted with multiplicity. For every fixed 0 < c <= 10^-5, we prove unconditionally that the lower limiting proportion of zeros whose two neighboring gaps are both strictly larger than 2pic/log X is at least 0.672468. Here X is the common height cutoff, and the neighbors belong to the full zero sequence. This refines Lamzouri's small-fixed-gap lower bound 0.6552... by explicitly implementing a shifted mollified-moment refinement of his approach. The proof combines a shifted mollified second-moment formula with Lamzouri's isolated-zero inequality. A positive shift bounds a truncated first moment of horizontal zero displacements, which is matched to an explicitly certified linear majorant of the projection deficit. We give the horizontal-boundary and global-height arguments, and derive a gap loss 6pi^2c^2 uniform over the necessary smoothing. The result is an explicit quantitative refinement using existing analytic inputs; no effective first height is obtained.
Author: Kim, Cheolmin
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225393754