Stopple's weak Newman conjecture for quadratic Dirichlet L-functions

For every fundamental discriminant $D\in\mathbb Z$, let $\Lambda_D$ be the associated De Bruijn–Newman constant. Weak Newman conjecture.

$$\sup_D\Lambda_D\geq0,$$

where the supremum is taken over all fundamental discriminants $D$. This weakens the individual assertion $\Lambda_D\geq0$ by requiring nonnegativity only somewhere in the family. The paper presents it as a variation investigated by Stopple; its resolution is not supplied in the given text.