A zero-density estimate with exponent 3(1−σ)/(2σ) for the Riemann zeta function
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…
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