We investigate Riemann's xi function $\xi(s):=\frac{1}{2}s(s-1)\pi^{-\frac{s}{2}}\Gamma(\frac{s}{2})\zeta(s)$ (here $\zeta(s)$ is the Riemann zeta function). The Hypothesis (RH) asserts that if $\xi(s)=0$, then $\mathrm{Re}(s)=\frac{1}{2}$. P\'olya proved RH equivalent to hyperbolicity of Jensen polynomials $J^{d,n}(X)$ constructed from certain Taylor coefficients $\xi(s)$. For each $d\geq 1$, ...

Grönwall's function \(G\) is defined for all natural numbers \(n>1\) by \(G(n)=\frac{\sigma(n)}{n \cdot \log n}\) where \(\sigma(n)\) the sum of divisors \(n\) and \(\log\) logarithm. We require properties extremely abundant numbers, that to say left right maxima \(n \mapsto G(n)\). also use colossally hyper numbers. There are several statements equivalent famous Riemann hypothesis. state hy...