{"id":"palomar/PALOMAR-2026-10-09-000005","url":"https://github.com/mrklwk/zeta-density-three-over-two-sigma-lean/tree/804bdb55b1fc40e6a1a6878fd96078644a70e288/lean","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-09-000005-v1.json","repo":"https://github.com/mrklwk/zeta-density-three-over-two-sigma-lean","tags":["math.NT","analytic-number-theory","riemann-zeta","zero-density"],"score":0,"title":"A zero-density estimate with exponent 3(1−σ)/(2σ) for the Riemann zeta function","trust":"high","domain":"math.NT","source":"palomar","authors":["Mark Lewko"],"reviews":0,"subject":"math.NT","summary":"For every real sigma>3/4 and epsilon>0 there exists C>0 such that for all real T>=2, all actual Riemann zeta zeros with Re(rho)>=sigma and |Im(rho)|<=T, counted with analytic multiplicity, number at most C*T^(3*(1-sigma)/(2*sigma)+epsilon). The proof combines separately proved Type I Dirichlet-polynomial large-values and critical-line twelfth-moment bounds. The companion moment is the literal integral on [0,3T] bounded by K*T^(2+epsilon), eventually in T. No analytic premise remains in the final endpoints. Compared with Tao–Trudgian–Yang Table 2 and Kerr Theorem 6, the leading exponent…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-09","reactions":{},"formalized":true,"formalizes":[{"title":"Selected Lean analytic proofs from Scott McColm repository, later pinned source","identifier":"https://github.com/smccolm/Lean/tree/6e2d10c6c2252ee1575bb7ef12dea12e2f1a3af1","relationship":"adapts"},{"title":"Selected Lean oscillatory, Abel/Jensen and contour proofs from earlier McColm pin","identifier":"https://github.com/smccolm/Lean/tree/2ace9e7c09a69fdcd1edae1ab6deb7cb3b4df1be","relationship":"adapts"},{"title":"Selected Fourier, Poisson, Mellin and Gamma proofs from prime-minor-arcs-2-15","identifier":"https://github.com/jconorgrogan/prime-minor-arcs-2-15/tree/f369f267b4dcfebf010c8e7baa2c9602e2960eba","relationship":"adapts"},{"title":"Heath-Brown (1978), twelfth-moment paper","identifier":"https://wiki.math.ntnu.no/_media/ma3001/2025h/analyticnumbertheory/heathbrowntwelfthmoment.pdf","relationship":"adapts"}]}