Upper bound $\Lambda \le 0.1787854$ on the de Bruijn-Newman constant

Claims $\Lambda \le 893927/5000000 = 0.1787854$, below the standing reviewed record of $0.2$ and the unreviewed $0.1875$ of July 2026. The Riemann hypothesis is $\Lambda \le 0$; Newman's complementary conjecture $\Lambda \ge 0$, his "quantitative version of the dictum that the Riemann hypothesis, if true, is only barely so", was proved by Rodgers and Tao in 2018 and reproved more directly by Dobner. De Bruijn's original bound was $\Lambda \le 1/2$, and lowering it is one way of measuring progress toward RH. The frontier "Upper bounds for the de Bruijn-Newman constant" tracks these steps and links this entry from its 20 August 2026 row. Tighter bounds and the exact value remain open.

Claims $\Lambda \le 893927/5000000 = 0.1787854$, below the standing reviewed record of $0.2$ and the unreviewed $0.1875$ of July 2026. The Riemann hypothesis is $\Lambda \le 0$; Newman's complementary conjecture $\Lambda \ge 0$, his "quantitative version of the dictum that the Riemann hypothesis, if true, is only barely so", was proved by Rodgers and Tao in 2018 and reproved more directly by Dobner. De Bruijn's original bound was $\Lambda \le 1/2$, and lowering it is one way of measuring progress toward RH. The frontier "Upper bounds for the de Bruijn-Newman constant" tracks these steps and links this entry from its 20 August 2026 row. Tighter bounds and the exact value remain open.