{"id":"palomar/PALOMAR-2026-10-21-000008","url":"https://github.com/mrklwk/zeta-density-39-over-17-lean/tree/c55fc0088bd4d7e61c5934abc5dd9153e8cb2f5d","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-21-000008-v1.json","repo":"https://github.com/mrklwk/zeta-density-39-over-17-lean","tags":["math.NT","msc:11M26","number-theory","riemann-zeta","zero-density","analytic-number-theory"],"score":0,"title":"Improved zero-density estimates for the Riemann zeta function","trust":"high","domain":"math.NT","source":"palomar","authors":["Mark Lewko"],"reviews":0,"subject":"math.NT","summary":"We establish improved zero-density estimates for the Riemann zeta function relative to the bounds previously released in PALOMAR-2026-10-11-000010 v1 and PALOMAR-2026-10-09-000005 v1. Let N(σ,T) count the nontrivial zeros with Re ρ ≥ σ and |Im ρ| ≤ T, with analytic multiplicity. For T ≥ 2 and ε > 0, our bounds have the form N(σ,T) ≤ C(σ,ε)T^((1−σ)A(σ)+ε). The native quantitative bounds improve those earlier power curves for 12/17 < σ ≤ 3/4 and 7/9 < σ ≤ 7/8. The displayed power-curve comparison continues for 7/8 < σ < 17/19, where the imported OpenAI result already gives N(σ,T)=0. Later…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-21","reactions":{},"formalized":true}