How long can an off-line zero survive the de Bruijn-Newman heat flow? An explicit unconditional lower bound for Lambda
Let $\Lambda$ be the de Bruijn-Newman constant. The Riemann hypothesis (RH) is equivalent to $\Lambda\le 0$, and Rodgers and Tao proved $\Lambda\ge 0$. We ask how small $\Lambda$ can be if $\zeta$ has a zero $1/2+\delta+i\gamma$ with $\delta>0$. We use de Bruijn's strip, the zero dynamics of the Polymath project, and an explicit local zero count for the heat-flow deformations $H_\tau$ that we prove here. With these we show unconditionally that $\Lambda \ge \delta^2/(70\log\gamma\log\log\gamma)$. Equivalently, every zero $\beta+i\gamma$ of $\zeta$ with $\gamma\ge 3\cdot 10^{12}$ satisfies…
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