de Bruijn-Newman constant

The de Bruijn-Newman constant $\Lambda$ is defined via the zeros of a certain function $H(\lambda,z)$, where $\lambda$ is a real parameter and $z$ is a complex variable. More precisely, $H(\lambda, z):=\int_{0}^{\infty} e^{\lambda u^{2}} \Phi(u) \cos (z u) \, du$, where $\Phi$ is the super-exponentially decaying function $\Phi(u) = \sum_{n=1}^{\infty} (2\pi^2n^4e^{9u}-3\pi n^2 e^{5u} ) e^{-\pi n^2 e^{4u}}$ and $\Lambda$ is the unique real number with the property that $H$ has only real zeros if and only if $\lambda\geq \Lambda$.

Lower bound: $\ge 0$
Upper bound: $\le 0.2$

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